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series</title> <meta name="description" content="Search results for: fourier series"> <meta name="keywords" content="fourier series"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler 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id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="fourier series"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 3505</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: fourier series</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3505</span> Degree of Approximation by the (T.E^1) Means of Conjugate Fourier Series in the Hölder Metric</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kejal%20Khatri">Kejal Khatri</a>, <a href="https://publications.waset.org/abstracts/search?q=Vishnu%20Narayan%20Mishra"> Vishnu Narayan Mishra</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20Fourier%20series" title="conjugate Fourier series">conjugate Fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20of%20approximation" title=" degree of approximation"> degree of approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=H%C3%B6lder%20metric" title=" Hölder metric"> Hölder metric</a>, <a href="https://publications.waset.org/abstracts/search?q=matrix%20summability" title=" matrix summability"> matrix summability</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20summability" title=" product summability"> product summability</a> </p> <a href="https://publications.waset.org/abstracts/2123/degree-of-approximation-by-the-te1-means-of-conjugate-fourier-series-in-the-holder-metric" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2123.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">420</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3504</span> Chebyshev Wavelets and Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emanuel%20Guariglia">Emanuel Guariglia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20wavelets" title="Chebyshev wavelets">Chebyshev wavelets</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20transform" title=" Fourier transform"> Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=connection%20coefficients" title=" connection coefficients"> connection coefficients</a>, <a href="https://publications.waset.org/abstracts/search?q=Taylor%20series" title=" Taylor series"> Taylor series</a>, <a href="https://publications.waset.org/abstracts/search?q=local%20fractional%20derivative" title=" local fractional derivative"> local fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=Cantor%20set" title=" Cantor set"> Cantor set</a> </p> <a href="https://publications.waset.org/abstracts/157194/chebyshev-wavelets-and-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/157194.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">123</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3503</span> Coefficients of Some Double Trigonometric Cosine and Sine Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jatinderdeep%20Kaur">Jatinderdeep Kaur</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the results of Kano from one-dimensional cosine and sine series are extended to two-dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as the class of semi convexity and class R are extended from one dimension to two dimensions. Under these extended classes, I have checked the function f(x,y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function. Further, some results are obtained which are the generalization of Moricz's results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20dirichlet%20kernel" title="conjugate dirichlet kernel">conjugate dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fejer%20kernel" title=" conjugate fejer kernel"> conjugate fejer kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20series" title=" fourier series"> fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=semi-convexity" title=" semi-convexity"> semi-convexity</a> </p> <a href="https://publications.waset.org/abstracts/32156/coefficients-of-some-double-trigonometric-cosine-and-sine-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32156.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">439</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3502</span> Improved Pitch Detection Using Fourier Approximation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Balachandra%20Kumaraswamy">Balachandra Kumaraswamy</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20G.%20Poonacha"> P. G. Poonacha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Automatic Music Information Retrieval has been one of the challenging topics of research for a few decades now with several interesting approaches reported in the literature. In this paper we have developed a pitch extraction method based on a finite Fourier series approximation to the given window of samples. We then estimate pitch as the fundamental period of the finite Fourier series approximation to the given window of samples. This method uses analysis of the strength of harmonics present in the signal to reduce octave as well as harmonic errors. The performance of our method is compared with three best known methods for pitch extraction, namely, Yin, Windowed Special Normalization of the Auto-Correlation Function and Harmonic Product Spectrum methods of pitch extraction. Our study with artificially created signals as well as music files show that Fourier Approximation method gives much better estimate of pitch with less octave and harmonic errors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=pitch" title="pitch">pitch</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20series" title=" fourier series"> fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=yin" title=" yin"> yin</a>, <a href="https://publications.waset.org/abstracts/search?q=normalization%20of%20the%20auto-%20correlation%20function" title=" normalization of the auto- correlation function"> normalization of the auto- correlation function</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20product" title=" harmonic product"> harmonic product</a>, <a href="https://publications.waset.org/abstracts/search?q=mean%20square%20error" title=" mean square error"> mean square error</a> </p> <a href="https://publications.waset.org/abstracts/36472/improved-pitch-detection-using-fourier-approximation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36472.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">413</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3501</span> Degree of Approximation of Functions Conjugate to Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of conjugate signals (functions) of functions belonging to different classes Lipα, Lip(α,p), Lip(ξ(t),p), W(Lr,ξ(t), (β ≥ 0)) by matrix summability means, lower triangular matrix operator, product means (i.e. (C,1)(E,1), (C,1)(E,q), (E,q)(C,1) (N,p,q)(E,1), and (E,q)(N,pn) of their conjugate trigonometric Fourier series. In this paper, we shall determine the degree of approximation of 2π-periodic function conjugate functions of f belonging to the function classes Lipα and W(Lr; ξ(t); (β ≥ 0)) by (C1.T) -means of their conjugate trigonometric Fourier series. On the other hand, we shall review above-mentioned work in the light of Lenski. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=signals" title="signals">signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20fourier%20approximation" title=" trigonometric fourier approximation"> trigonometric fourier approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=class%20W%28L%5Er" title=" class W(L^r"> class W(L^r</a>, <a href="https://publications.waset.org/abstracts/search?q=%5Cxi%28t%29" title="\xi(t)">\xi(t)</a>, <a href="https://publications.waset.org/abstracts/search?q=conjugate%20fourier%20series" title=" conjugate fourier series"> conjugate fourier series</a> </p> <a href="https://publications.waset.org/abstracts/20996/degree-of-approximation-of-functions-conjugate-to-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20996.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">397</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3500</span> Degree of Approximation of Functions by Product Means</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hare%20Krishna%20Nigam">Hare Krishna Nigam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, for the first time, (E,q)(C,2) product summability method is introduced and two quite new results on degree of approximation of the function f belonging to Lip (alpha,r)class and W(L(r), xi(t)) class by (E,q)(C,2) product means of Fourier series, has been obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Degree%20of%20approximation" title="Degree of approximation">Degree of approximation</a>, <a href="https://publications.waset.org/abstracts/search?q=%28E" title=" (E"> (E</a>, <a href="https://publications.waset.org/abstracts/search?q=q%29%28C" title="q)(C">q)(C</a>, <a href="https://publications.waset.org/abstracts/search?q=2%29%20means" title="2) means">2) means</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20series" title=" Fourier series"> Fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=Lebesgue%20integral" title=" Lebesgue integral"> Lebesgue integral</a>, <a href="https://publications.waset.org/abstracts/search?q=Lip%20%28alpha" title=" Lip (alpha"> Lip (alpha</a>, <a href="https://publications.waset.org/abstracts/search?q=r%29class" title="r)class">r)class</a>, <a href="https://publications.waset.org/abstracts/search?q=W%28L%28r%29" title=" W(L(r)"> W(L(r)</a>, <a href="https://publications.waset.org/abstracts/search?q=xi%28t%29%29class%20of%20%20functions" title="xi(t))class of functions">xi(t))class of functions</a> </p> <a href="https://publications.waset.org/abstracts/32235/degree-of-approximation-of-functions-by-product-means" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32235.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">518</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3499</span> Modeling of Diurnal Pattern of Air Temperature in a Tropical Environment: Ile-Ife and Ibadan, Nigeria</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rufus%20Temidayo%20Akinnubi">Rufus Temidayo Akinnubi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Adeniyi"> M. O. Adeniyi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Existing diurnal air temperature models simulate night time air temperature over Nigeria with high biases. An improved parameterization is presented for modeling the diurnal pattern of air temperature (Ta) which is applicable in the calculation of turbulent heat fluxes in Global climate models, based on Nigeria Micrometeorological Experimental site (NIMEX) surface layer observations. Five diurnal Ta models for estimating hourly Ta from daily maximum, daily minimum, and daily mean air temperature were validated using root-mean-square error (RMSE), Mean Error Bias (MBE) and scatter graphs. The original Fourier series model showed better performance for unstable air temperature parameterizations while the stable Ta was strongly overestimated with a large error. The model was improved with the inclusion of the atmospheric cooling rate that accounts for the temperature inversion that occurs during the nocturnal boundary layer condition. The MBE and RMSE estimated by the modified Fourier series model reduced by 4.45 oC and 3.12 oC during the transitional period from dry to wet stable atmospheric conditions. The modified Fourier series model gave good estimation of the diurnal weather patterns of Ta when compared with other existing models for a tropical environment. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=air%20temperature" title="air temperature">air temperature</a>, <a href="https://publications.waset.org/abstracts/search?q=mean%20bias%20error" title=" mean bias error"> mean bias error</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20series%20analysis" title=" Fourier series analysis"> Fourier series analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=surface%20energy%20balance" title=" surface energy balance"> surface energy balance</a>, <a href="https://publications.waset.org/abstracts/search?q=" title=" "> </a> </p> <a href="https://publications.waset.org/abstracts/75489/modeling-of-diurnal-pattern-of-air-temperature-in-a-tropical-environment-ile-ife-and-ibadan-nigeria" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/75489.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">230</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3498</span> On Fourier Type Integral Transform for a Class of Generalized Quotients</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20S.%20Issa">A. S. Issa</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20K.%20Q.%20AL-Omari"> S. K. Q. AL-Omari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Boehmian" title="Boehmian">Boehmian</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20integral" title=" Fourier integral"> Fourier integral</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20type%20integral" title=" Fourier type integral"> Fourier type integral</a>, <a href="https://publications.waset.org/abstracts/search?q=generalized%20quotient" title=" generalized quotient"> generalized quotient</a> </p> <a href="https://publications.waset.org/abstracts/45947/on-fourier-type-integral-transform-for-a-class-of-generalized-quotients" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45947.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">365</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3497</span> Approximation of Periodic Functions Belonging to Lipschitz Classes by Product Matrix Means of Fourier Series</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Smita%20Sonker">Smita Sonker</a>, <a href="https://publications.waset.org/abstracts/search?q=Uaday%20Singh"> Uaday Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lipschitz%20classes" title="Lipschitz classes">Lipschitz classes</a>, <a href="https://publications.waset.org/abstracts/search?q=product%20matrix%20operator" title=" product matrix operator"> product matrix operator</a>, <a href="https://publications.waset.org/abstracts/search?q=signals" title=" signals"> signals</a>, <a href="https://publications.waset.org/abstracts/search?q=trigonometric%20Fourier%20approximation" title=" trigonometric Fourier approximation"> trigonometric Fourier approximation</a> </p> <a href="https://publications.waset.org/abstracts/4757/approximation-of-periodic-functions-belonging-to-lipschitz-classes-by-product-matrix-means-of-fourier-series" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4757.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">478</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3496</span> Series "H154M" as a Unit Area of the Region between the Lines and Curves</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hisyam%20Hidayatullah">Hisyam Hidayatullah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This world events consciously or not realize everything has a pattern, until the events of the universe according to the Big Bang theory of the solar system which makes so regular in the rotation. The author would like to create a results curve area between the quadratic function y=kx2 and line y=ka2 using GeoGebra application version 4.2. This paper can provide a series that is no less interesting with Fourier series, so that will add new material about the series can be calculated with sigma notation. In addition, the ranks of the unique natural numbers of extensive changes in established areas. Finally, this paper provides analytical and geometric proof of the vast area in between the lines and curves that give the area is formed by y=ka2 dan kurva y=kx2, x-axis, line x=√a and x=-√a make a series of numbers for k=1 and a ∈ original numbers. ∑_(i=0)^n=(4n√n)/3=0+4/3+(8√2)/3+4√3+⋯+(4n√n)/3. The author calls the series “H154M”. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sequence" title="sequence">sequence</a>, <a href="https://publications.waset.org/abstracts/search?q=series" title=" series"> series</a>, <a href="https://publications.waset.org/abstracts/search?q=sigma%20notation" title=" sigma notation"> sigma notation</a>, <a href="https://publications.waset.org/abstracts/search?q=application%20GeoGebra" title=" application GeoGebra"> application GeoGebra</a> </p> <a href="https://publications.waset.org/abstracts/10358/series-h154m-as-a-unit-area-of-the-region-between-the-lines-and-curves" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10358.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">376</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3495</span> L1-Convergence of Modified Trigonometric Sums</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sandeep%20Kaur%20Chouhan">Sandeep Kaur Chouhan</a>, <a href="https://publications.waset.org/abstracts/search?q=Jatinderdeep%20Kaur"> Jatinderdeep Kaur</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20S.%20Bhatia"> S. S. Bhatia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conjugate%20Dirichlet%20kernel" title="conjugate Dirichlet kernel">conjugate Dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=Dirichlet%20kernel" title=" Dirichlet kernel"> Dirichlet kernel</a>, <a href="https://publications.waset.org/abstracts/search?q=L1-convergence" title=" L1-convergence"> L1-convergence</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20sums" title=" modified sums"> modified sums</a> </p> <a href="https://publications.waset.org/abstracts/44182/l1-convergence-of-modified-trigonometric-sums" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44182.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">355</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3494</span> Frequency Identification of Wiener-Hammerstein Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brouri%20Adil">Brouri Adil</a>, <a href="https://publications.waset.org/abstracts/search?q=Giri%20Fouad"> Giri Fouad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wiener-Hammerstein%20systems" title="Wiener-Hammerstein systems">Wiener-Hammerstein systems</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20series%20expansions" title=" Fourier series expansions"> Fourier series expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20identification" title=" frequency identification"> frequency identification</a>, <a href="https://publications.waset.org/abstracts/search?q=automation%20science" title=" automation science"> automation science</a> </p> <a href="https://publications.waset.org/abstracts/7941/frequency-identification-of-wiener-hammerstein-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7941.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">537</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3493</span> Double Fourier Series Applied to Supraharmonic Determination: The Specific Cases of a Boost and an Interleaved Boost Converter Used as Active Power Factor Correctors</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Erzen%20Muharemi">Erzen Muharemi</a>, <a href="https://publications.waset.org/abstracts/search?q=Emmanuel%20De%20Jaeger"> Emmanuel De Jaeger</a>, <a href="https://publications.waset.org/abstracts/search?q=Jos%20Knockaert"> Jos Knockaert</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The work presented here investigates the modeling of power electronics converters in terms of their harmonic production. Specifically, it addresses high-frequency emissions in the range of 2-150 kHz, referred to as supraharmonics. This paper models a conventional converter, namely the boost converter used as an active power factor corrector (APFC). Furthermore, the modeling is extended to the case of the interleaved boost converter, which offers advantages such as halving the emissions. Finally, a comparison between the theoretical, numerical, and experimental results will be provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=APFC" title="APFC">APFC</a>, <a href="https://publications.waset.org/abstracts/search?q=boost%20converter" title=" boost converter"> boost converter</a>, <a href="https://publications.waset.org/abstracts/search?q=converter%20modeling" title=" converter modeling"> converter modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20fourier%20series" title=" double fourier series"> double fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=supraharmonics" title=" supraharmonics"> supraharmonics</a> </p> <a href="https://publications.waset.org/abstracts/188253/double-fourier-series-applied-to-supraharmonic-determination-the-specific-cases-of-a-boost-and-an-interleaved-boost-converter-used-as-active-power-factor-correctors" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188253.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">42</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3492</span> Solution of Some Boundary Value Problems of the Generalized Theory of Thermo-Piezoelectricity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manana%20Chumburidze">Manana Chumburidze</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=thermo-piezoelectricity" title="thermo-piezoelectricity">thermo-piezoelectricity</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problems" title=" boundary value problems"> boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%27s%20series" title=" Fourier's series"> Fourier's series</a>, <a href="https://publications.waset.org/abstracts/search?q=isotropic%20homogeneous%20elastic%20media" title=" isotropic homogeneous elastic media "> isotropic homogeneous elastic media </a> </p> <a href="https://publications.waset.org/abstracts/33983/solution-of-some-boundary-value-problems-of-the-generalized-theory-of-thermo-piezoelectricity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33983.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">465</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3491</span> Multi-Scale Modelling of Thermal Wrinkling of Thin Membranes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Salim%20Belouettar">Salim Belouettar</a>, <a href="https://publications.waset.org/abstracts/search?q=Kodjo%20Attipou"> Kodjo Attipou</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The thermal wrinkling behavior of thin membranes is investigated. The Fourier double scale series are used to deduce the macroscopic membrane wrinkling equations. The obtained equations account for the global and local wrinkling modes. Numerical examples are conducted to assess the validity of the approach developed. Compared to the finite element full model, the present model needs only few degrees of freedom to recover accurately the bifurcation curves and wrinkling paths. Different parameters such as membrane’s aspect ratio, wave number, pre-stressed membranes are discussed from a numerical point of view and the properties of the wrinkles (critical load, wavelength, size and location) are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=wrinkling" title="wrinkling">wrinkling</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20stresses" title=" thermal stresses"> thermal stresses</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20series" title=" Fourier series"> Fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=thin%20membranes" title=" thin membranes"> thin membranes</a> </p> <a href="https://publications.waset.org/abstracts/17997/multi-scale-modelling-of-thermal-wrinkling-of-thin-membranes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17997.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">391</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3490</span> Application of Fourier Series Based Learning Control on Mechatronic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sandra%20Ba%C3%9Fler">Sandra Baßler</a>, <a href="https://publications.waset.org/abstracts/search?q=Peter%20D%C3%BCnow"> Peter Dünow</a>, <a href="https://publications.waset.org/abstracts/search?q=Mathias%20Marquardt"> Mathias Marquardt</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A Fourier series based learning control (FSBLC) algorithm for tracking trajectories of mechanical systems with unknown nonlinearities is presented. Two processes are introduced to which the FSBLC with PD controller is applied. One is a simplified service robot capable of climbing stairs due to special wheels and the other is a propeller driven pendulum with nearly the same requirements on control. Additionally to the investigation of learning the feed forward for the desired trajectories some considerations on the implementation of such an algorithm on low cost microcontroller hardware are made. Simulations of the service robot as well as practical experiments on the pendulum show the capability of the used FSBLC algorithm to perform the task of improving control behavior for repetitive task of such mechanical systems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=climbing%20stairs" title="climbing stairs">climbing stairs</a>, <a href="https://publications.waset.org/abstracts/search?q=FSBLC" title=" FSBLC"> FSBLC</a>, <a href="https://publications.waset.org/abstracts/search?q=ILC" title=" ILC"> ILC</a>, <a href="https://publications.waset.org/abstracts/search?q=service%20robot" title=" service robot"> service robot</a> </p> <a href="https://publications.waset.org/abstracts/47470/application-of-fourier-series-based-learning-control-on-mechatronic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47470.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">314</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3489</span> The Optical OFDM Equalization Based on the Fractional Fourier Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Cherifi">A. Cherifi</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20S.%20Bouazza"> B. S. Bouazza</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20O.%20Dahman"> A. O. Dahman</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Yagoubi"> B. Yagoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=OFDM" title="OFDM">OFDM</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20fourier%20transform" title=" fractional fourier transform"> fractional fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=internet%20and%20information%20technology" title=" internet and information technology"> internet and information technology</a> </p> <a href="https://publications.waset.org/abstracts/27211/the-optical-ofdm-equalization-based-on-the-fractional-fourier-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27211.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">406</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3488</span> Equalization Algorithm for the Optical OFDM System Based on the Fractional Fourier Transform </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Cherifi">A. Cherifi</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Bouazza"> B. Bouazza</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20O.%20Dahmane"> A. O. Dahmane</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Yagoubi"> B. Yagoubi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Transmission over Optical channels will introduce inter-symbol interference (ISI) as well as inter-channel (or inter-carrier) interference (ICI). To decrease the effects of ICI, this paper proposes equalizer for the Optical OFDM system based on the fractional Fourier transform (FrFFT). In this FrFT-OFDM system, traditional Fourier transform is replaced by fractional Fourier transform to modulate and demodulate the data symbols. The equalizer proposed consists of sampling the received signal in the different time per time symbol. Theoretical analysis and numerical simulation are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=OFDM" title="OFDM">OFDM</a>, <a href="https://publications.waset.org/abstracts/search?q=%28FrFT%29%20fractional%20fourier%20transform" title=" (FrFT) fractional fourier transform"> (FrFT) fractional fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20OFDM" title=" optical OFDM"> optical OFDM</a>, <a href="https://publications.waset.org/abstracts/search?q=equalization%20algorithm" title=" equalization algorithm"> equalization algorithm</a> </p> <a href="https://publications.waset.org/abstracts/23848/equalization-algorithm-for-the-optical-ofdm-system-based-on-the-fractional-fourier-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23848.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">430</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3487</span> Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fethi%20Soltani">Fethi Soltani</a>, <a href="https://publications.waset.org/abstracts/search?q=Adel%20Almarashi"> Adel Almarashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Idir%20Mechai"> Idir Mechai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourier%20multiplier%20operators" title="fourier multiplier operators">fourier multiplier operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Gauss-Kronrod%20method%20of%20integration" title=" Gauss-Kronrod method of integration"> Gauss-Kronrod method of integration</a>, <a href="https://publications.waset.org/abstracts/search?q=Paley-Wiener%20space" title=" Paley-Wiener space"> Paley-Wiener space</a>, <a href="https://publications.waset.org/abstracts/search?q=Tikhonov%20regularization" title=" Tikhonov regularization"> Tikhonov regularization</a> </p> <a href="https://publications.waset.org/abstracts/38538/numerical-applications-of-tikhonov-regularization-for-the-fourier-multiplier-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38538.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">318</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3486</span> An Adaptive Decomposition for the Variability Analysis of Observation Time Series in Geophysics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Olivier%20Delage">Olivier Delage</a>, <a href="https://publications.waset.org/abstracts/search?q=Thierry%20Portafaix"> Thierry Portafaix</a>, <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Bencherif"> Hassan Bencherif</a>, <a href="https://publications.waset.org/abstracts/search?q=Guillaume%20Guimbretiere"> Guillaume Guimbretiere</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Most observation data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series in geophysics have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at all time-scales and require a time-frequency representation to analyze their variability. Empirical Mode Decomposition (EMD) is a relatively new technic as part of a more general signal processing method called the Hilbert-Huang transform. This analysis method turns out to be particularly suitable for non-linear and non-stationary signals and consists in decomposing a signal in an auto adaptive way into a sum of oscillating components named IMFs (Intrinsic Mode Functions), and thereby acts as a bank of bandpass filters. The advantages of the EMD technic are to be entirely data driven and to provide the principal variability modes of the dynamics represented by the original time series. However, the main limiting factor is the frequency resolution that may give rise to the mode mixing phenomenon where the spectral contents of some IMFs overlap each other. To overcome this problem, J. Gilles proposed an alternative entitled “Empirical Wavelet Transform” (EWT) which consists in building from the segmentation of the original signal Fourier spectrum, a bank of filters. The method used is based on the idea utilized in the construction of both Littlewood-Paley and Meyer’s wavelets. The heart of the method lies in the segmentation of the Fourier spectrum based on the local maxima detection in order to obtain a set of non-overlapping segments. Because linked to the Fourier spectrum, the frequency resolution provided by EWT is higher than that provided by EMD and therefore allows to overcome the mode-mixing problem. On the other hand, if the EWT technique is able to detect the frequencies involved in the original time series fluctuations, EWT does not allow to associate the detected frequencies to a specific mode of variability as in the EMD technic. Because EMD is closer to the observation of physical phenomena than EWT, we propose here a new technic called EAWD (Empirical Adaptive Wavelet Decomposition) based on the coupling of the EMD and EWT technics by using the IMFs density spectral content to optimize the segmentation of the Fourier spectrum required by EWT. In this study, EMD and EWT technics are described, then EAWD technic is presented. Comparison of results obtained respectively by EMD, EWT and EAWD technics on time series of ozone total columns recorded at Reunion island over [1978-2019] period is discussed. This study was carried out as part of the SOLSTYCE project dedicated to the characterization and modeling of the underlying dynamics of time series issued from complex systems in atmospheric sciences <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20filtering" title="adaptive filtering">adaptive filtering</a>, <a href="https://publications.waset.org/abstracts/search?q=empirical%20mode%20decomposition" title=" empirical mode decomposition"> empirical mode decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=empirical%20wavelet%20transform" title=" empirical wavelet transform"> empirical wavelet transform</a>, <a href="https://publications.waset.org/abstracts/search?q=filter%20banks" title=" filter banks"> filter banks</a>, <a href="https://publications.waset.org/abstracts/search?q=mode-mixing" title=" mode-mixing"> mode-mixing</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20and%20non-stationary%20time%20series" title=" non-linear and non-stationary time series"> non-linear and non-stationary time series</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet" title=" wavelet"> wavelet</a> </p> <a href="https://publications.waset.org/abstracts/128255/an-adaptive-decomposition-for-the-variability-analysis-of-observation-time-series-in-geophysics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/128255.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">137</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3485</span> Construction of Graph Signal Modulations via Graph Fourier Transform and Its Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xianwei%20Zheng">Xianwei Zheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang"> Yuan Yan Tang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signals" title="graph signals">graph signals</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20transform" title=" windowed graph Fourier transform"> windowed graph Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20frames" title=" windowed graph Fourier frames"> windowed graph Fourier frames</a>, <a href="https://publications.waset.org/abstracts/search?q=vertex%20frequency%20analysis" title=" vertex frequency analysis"> vertex frequency analysis</a> </p> <a href="https://publications.waset.org/abstracts/63133/construction-of-graph-signal-modulations-via-graph-fourier-transform-and-its-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">342</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3484</span> Factors Influencing the Acceptance of Y Series among the Residents in Three Southern Border Provinces of Thailand</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chetsada%20Noknoi">Chetsada Noknoi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The acceptance of Y series refers to the willingness and enjoyment of watching Y series without feeling different from general series. This occurs when people watch Y series and derive happiness and entertainment from it. The viewing experience has the most significant impact on Y series acceptance. This research aims to 1) investigate the levels of acceptance of sexual diversity, image of Y series Actors, media exposure, and Y series acceptance among the residents in three southern border provinces of Thailand, and 2) examine how acceptance of sexual diversity, actor perceptions in Y series, and media exposure influence Y series acceptance in these provinces. The sample consisted of 322 participants from the three southern border provinces of Thailand. The research instrument used was a questionnaire, and data were analyzed using frequency, percentage, mean, standard deviation, and multiple regression analysis. The findings revealed that overall, acceptance of sexual diversity, Image of Y series Actors, and Y series acceptance among the residents in three southern border provinces of Thailand were at a high level, while media exposure was moderate overall. However, the two factors that had the most significant impact on Y series acceptance in these provinces, ranked from highest to lowest influence, were media exposure and acceptance of sexual diversity. Both of these factors had a positive effect on Y series acceptance among the residents in three southern border provinces of Thailand. Collectively, these factors accounted for 40.7% of the variance in Y series acceptance among the residents in three southern border provinces of Thailand. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=acceptance" title="acceptance">acceptance</a>, <a href="https://publications.waset.org/abstracts/search?q=acceptance%20of%20sexual%20diversity" title=" acceptance of sexual diversity"> acceptance of sexual diversity</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20of%20Y%20series%20actors" title=" image of Y series actors"> image of Y series actors</a>, <a href="https://publications.waset.org/abstracts/search?q=media%20exposure" title=" media exposure"> media exposure</a>, <a href="https://publications.waset.org/abstracts/search?q=Y%20series" title=" Y series"> Y series</a> </p> <a href="https://publications.waset.org/abstracts/174083/factors-influencing-the-acceptance-of-y-series-among-the-residents-in-three-southern-border-provinces-of-thailand" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/174083.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">77</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3483</span> Content Analysis and Attitude of Thai Students towards Thai Series “Hormones: Season 2”</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Siriporn%20Meenanan">Siriporn Meenanan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The objective of this study is to investigate the attitude of Thai students towards the Thai series "Hormones the Series Season 2". This study was conducted in the quantitative research, and the questionnaires were used to collect data from 400 people of the sample group. Descriptive statistics were used in data analysis. The findings reveal that most participants have positive comments regarding the series. They strongly agreed that the series reflects on the way of life and problems of teenagers in Thailand. Hence, the participants believe that if adults have a chance to watch the series, they will have the better understanding of the teenagers. In addition, the participants also agreed that the contents of the play are appropriate and satisfiable as the contents of “Hormones the Series Season 2” will raise awareness among the teens and use it as a guide to prevent problems that might happen during their teenage life. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=content%20analysis" title="content analysis">content analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=attitude" title=" attitude"> attitude</a>, <a href="https://publications.waset.org/abstracts/search?q=Thai%20series" title=" Thai series"> Thai series</a>, <a href="https://publications.waset.org/abstracts/search?q=hormones%20the%20Series" title=" hormones the Series"> hormones the Series</a> </p> <a href="https://publications.waset.org/abstracts/39934/content-analysis-and-attitude-of-thai-students-towards-thai-series-hormones-season-2" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/39934.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">229</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3482</span> Jacobson Semisimple Skew Inverse Laurent Series Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Moussavi">Ahmad Moussavi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=skew%20polynomial%20rings" title="skew polynomial rings">skew polynomial rings</a>, <a href="https://publications.waset.org/abstracts/search?q=Laurent%20series" title=" Laurent series"> Laurent series</a>, <a href="https://publications.waset.org/abstracts/search?q=skew%20inverse%20Laurent%20series%20rings" title=" skew inverse Laurent series rings"> skew inverse Laurent series rings</a> </p> <a href="https://publications.waset.org/abstracts/128005/jacobson-semisimple-skew-inverse-laurent-series-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/128005.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">165</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3481</span> Estimation of Fourier Coefficients of Flux Density for Surface Mounted Permanent Magnet (SMPM) Generators by Direct Search Optimization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramakrishna%20Rao%20Mamidi">Ramakrishna Rao Mamidi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is essential for Surface Mounted Permanent Magnet (SMPM) generators to determine the performance prediction and analyze the magnet’s air gap flux density wave shape. The flux density wave shape is neither a pure sine wave or square wave nor a combination. This is due to the variation of air gap reluctance between the stator and permanent magnets. The stator slot openings and the number of slots make the wave shape highly complicated. To reduce the complexity of analysis, approximations are made to the wave shape using Fourier analysis. In contrast to the traditional integration method, the Fourier coefficients, an and bn, are obtained by direct search method optimization. The wave shape with optimized coefficients gives a wave shape close to the desired wave shape. Harmonics amplitudes are worked out and compared with initial values. It can be concluded that the direct search method can be used for estimating Fourier coefficients for irregular wave shapes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=direct%20search" title="direct search">direct search</a>, <a href="https://publications.waset.org/abstracts/search?q=flux%20plot" title=" flux plot"> flux plot</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20analysis" title=" fourier analysis"> fourier analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=permanent%20magnets" title=" permanent magnets"> permanent magnets</a> </p> <a href="https://publications.waset.org/abstracts/139812/estimation-of-fourier-coefficients-of-flux-density-for-surface-mounted-permanent-magnet-smpm-generators-by-direct-search-optimization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/139812.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">216</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3480</span> Electricity Load Modeling: An Application to Italian Market</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Giovanni%20Masala">Giovanni Masala</a>, <a href="https://publications.waset.org/abstracts/search?q=Stefania%20Marica"> Stefania Marica</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Forecasting electricity load plays a crucial role regards decision making and planning for economical purposes. Besides, in the light of the recent privatization and deregulation of the power industry, the forecasting of future electricity load turned out to be a very challenging problem. Empirical data about electricity load highlights a clear seasonal behavior (higher load during the winter season), which is partly due to climatic effects. We also emphasize the presence of load periodicity at a weekly basis (electricity load is usually lower on weekends or holidays) and at daily basis (electricity load is clearly influenced by the hour). Finally, a long-term trend may depend on the general economic situation (for example, industrial production affects electricity load). All these features must be captured by the model. The purpose of this paper is then to build an hourly electricity load model. The deterministic component of the model requires non-linear regression and Fourier series while we will investigate the stochastic component through econometrical tools. The calibration of the parameters’ model will be performed by using data coming from the Italian market in a 6 year period (2007- 2012). Then, we will perform a Monte Carlo simulation in order to compare the simulated data respect to the real data (both in-sample and out-of-sample inspection). The reliability of the model will be deduced thanks to standard tests which highlight a good fitting of the simulated values. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ARMA-GARCH%20process" title="ARMA-GARCH process">ARMA-GARCH process</a>, <a href="https://publications.waset.org/abstracts/search?q=electricity%20load" title=" electricity load"> electricity load</a>, <a href="https://publications.waset.org/abstracts/search?q=fitting%20tests" title=" fitting tests"> fitting tests</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier%20series" title=" Fourier series"> Fourier series</a>, <a href="https://publications.waset.org/abstracts/search?q=Monte%20Carlo%20simulation" title=" Monte Carlo simulation"> Monte Carlo simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20regression" title=" non-linear regression"> non-linear regression</a> </p> <a href="https://publications.waset.org/abstracts/11709/electricity-load-modeling-an-application-to-italian-market" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11709.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">395</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3479</span> A Study on Hierarchy and Popularity of Foreign TV Series with Different Origin Countries among Chinese Audiences from a Uses and Gratification Perspective</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Terigele">Terigele</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Cultural products are always shelved into different classes of a hierarchy that separates so-called highbrow and lowbrow cultures. This study illustrated that audiences might even construct a hierarchy according to the origin countries when consuming certain products. Chinese audiences now have access to TV series from all around the world thanks to the internet. TV series from different origin countries show some particular features in terms of length, theme, plots, accessibility, seriousness etc. Their audiences were therefore stereotyped because of what they watch. Based on in-depth interviews with 20 participants, this research has following findings: 1) Most popular origin countries of foreign TV series in China are Korea, the United States, the United Kingdom, Japan and European countries in a descending order. Korean TV series are most popular because they are less serious and more accessible compared to others. 2) In the hierarchy of the TV series, European TV series stand on the top followed by British and American TV series. Japanese TV series are also categorized into highbrow class. Korean TV series are at the bottom and always seen as lowbrow cultural products. 3) Most audiences consume TV series from more than one origin countries and have different needs when watching them. Participants reported that they watch European TV series because those TV series are more artistic than their counterparts and of great quality. They watch British and American TV series mainly to improve their English and to learn about the culture. They find Japanese TV series very enjoyable with a large variety of themes and impressive lines. Audiences watch Korean TV series mostly to entertain and kill time. 4) Audiences do care about cultural taste. Especially those who watch European, British and American TV series usually tend to consider audiences who watch nothing but Korean TV series to be shallow. On the other hand, Korean TV series’ audiences seem to care less about the hierarchy of the TV series. Even when they discuss the hierarchy, they tend to accept the judgments with ironies and jokes. Future studies can dig deeply into the genre and content of TV series with different origin countries and also investigate more about the psychology of audiences regarding the gender, age, education, socioeconomic status etc. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=foreign%20TV%20series" title="foreign TV series">foreign TV series</a>, <a href="https://publications.waset.org/abstracts/search?q=hierarchy" title=" hierarchy"> hierarchy</a>, <a href="https://publications.waset.org/abstracts/search?q=popularity" title=" popularity"> popularity</a>, <a href="https://publications.waset.org/abstracts/search?q=uses%20and%20gratification" title=" uses and gratification"> uses and gratification</a> </p> <a href="https://publications.waset.org/abstracts/53622/a-study-on-hierarchy-and-popularity-of-foreign-tv-series-with-different-origin-countries-among-chinese-audiences-from-a-uses-and-gratification-perspective" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53622.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">243</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3478</span> Mathematical Reconstruction of an Object Image Using X-Ray Interferometric Fourier Holography Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20K.%20Balyan">M. K. Balyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamical%20diffraction" title="dynamical diffraction">dynamical diffraction</a>, <a href="https://publications.waset.org/abstracts/search?q=hologram" title=" hologram"> hologram</a>, <a href="https://publications.waset.org/abstracts/search?q=object%20image" title=" object image"> object image</a>, <a href="https://publications.waset.org/abstracts/search?q=X-ray%20holography" title=" X-ray holography"> X-ray holography</a> </p> <a href="https://publications.waset.org/abstracts/56283/mathematical-reconstruction-of-an-object-image-using-x-ray-interferometric-fourier-holography-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56283.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">394</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3477</span> Convergence Results of Two-Dimensional Homogeneous Elastic Plates from Truncation of Potential Energy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Erick%20Pruchnicki">Erick Pruchnicki</a>, <a href="https://publications.waset.org/abstracts/search?q=Nikhil%20Padhye"> Nikhil Padhye</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Plates are important engineering structures which have attracted extensive research since the 19th century. The subject of this work is statical analysis of a linearly elastic homogenous plate under small deformations. A 'thin plate' is a three-dimensional structure comprising of a small transverse dimension with respect to a flat mid-surface. The general aim of any plate theory is to deduce a two-dimensional model, in terms of mid-surface quantities, to approximately and accurately describe the plate's deformation in terms of mid-surface quantities. In recent decades, a common starting point for this purpose is to utilize series expansion of a displacement field across the thickness dimension in terms of the thickness parameter (h). These attempts are mathematically consistent in deriving leading-order plate theories based on certain a priori scaling between the thickness and the applied loads; for example, asymptotic methods which are aimed at generating leading-order two-dimensional variational problems by postulating formal asymptotic expansion of the displacement fields. Such methods rigorously generate a hierarchy of two-dimensional models depending on the order of magnitude of the applied load with respect to the plate-thickness. However, in practice, applied loads are external and thus not directly linked or dependent on the geometry/thickness of the plate; thus, rendering any such model (based on a priori scaling) of limited practical utility. In other words, the main limitation of these approaches is that they do not furnish a single plate model for all orders of applied loads. Following analogy of recent efforts of deploying Fourier-series expansion to study convergence of reduced models, we propose two-dimensional model(s) resulting from truncation of the potential energy and rigorously prove the convergence of these two-dimensional plate models to the parent three-dimensional linear elasticity with increasing truncation order of the potential energy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=plate%20theory" title="plate theory">plate theory</a>, <a href="https://publications.waset.org/abstracts/search?q=Fourier-series%20expansion" title=" Fourier-series expansion"> Fourier-series expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20result" title=" convergence result"> convergence result</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomials" title=" Legendre polynomials"> Legendre polynomials</a> </p> <a href="https://publications.waset.org/abstracts/124096/convergence-results-of-two-dimensional-homogeneous-elastic-plates-from-truncation-of-potential-energy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124096.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">113</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3476</span> Digital Material Characterization Using the Quantum Fourier Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Felix%20Givois">Felix Givois</a>, <a href="https://publications.waset.org/abstracts/search?q=Nicolas%20R.%20Gauger"> Nicolas R. Gauger</a>, <a href="https://publications.waset.org/abstracts/search?q=Matthias%20Kabel"> Matthias Kabel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The efficient digital material characterization is of great interest to many fields of application. It consists of the following three steps. First, a 3D reconstruction of 2D scans must be performed. Then, the resulting gray-value image of the material sample is enhanced by image processing methods. Finally, partial differential equations (PDE) are solved on the segmented image, and by averaging the resulting solutions fields, effective properties like stiffness or conductivity can be computed. Due to the high resolution of current CT images, the latter is typically performed with matrix-free solvers. Among them, a solver that uses the explicit formula of the Green-Eshelby operator in Fourier space has been proposed by Moulinec and Suquet. Its algorithmic, most complex part is the Fast Fourier Transformation (FFT). In our talk, we will discuss the potential quantum advantage that can be obtained by replacing the FFT with the Quantum Fourier Transformation (QFT). We will especially show that the data transfer for noisy intermediate-scale quantum (NISQ) devices can be improved by using appropriate boundary conditions for the PDE, which also allows using semi-classical versions of the QFT. In the end, we will compare the results of the QFT-based algorithm for simple geometries with the results of the FFT-based homogenization method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=most%20likelihood%20amplitude%20estimation%20%28MLQAE%29" title="most likelihood amplitude estimation (MLQAE)">most likelihood amplitude estimation (MLQAE)</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20homogenization" title=" numerical homogenization"> numerical homogenization</a>, <a href="https://publications.waset.org/abstracts/search?q=quantum%20Fourier%20transformation%20%28QFT%29" title=" quantum Fourier transformation (QFT)"> quantum Fourier transformation (QFT)</a>, <a href="https://publications.waset.org/abstracts/search?q=NISQ%20devises" title=" NISQ devises"> NISQ devises</a> </p> <a href="https://publications.waset.org/abstracts/163241/digital-material-characterization-using-the-quantum-fourier-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163241.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">78</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourier%20series&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourier%20series&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=fourier%20series&page=4">4</a></li> <li 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