CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "publications.waset.org",cType: 'managed',cRay: '919f5cb8dbc8cdfe',cH: 'v8x42hKr.2jta_Z8RBILVGhtX2PwLWQRbFuJi2MJh5I-1740902444-1.2.1.1-.8QqVyzY4dN95qBd2dZQOKb3RSYddA5BGfIMn4u6mihxWGDM4dPQJ8alRVavB7CE',cUPMDTk: "\/search?q=Fractional%20Fourier%20Transform&__cf_chl_tk=d2_cPVuUSlh3Jt81b.s6JM9nZtMSlaI31zVosMLAXUg-1740902444-1.0.1.1-6ug2LNrZ367yJO_N9Y7a0QwbFuTKF64xStliFZxcqcc",cFPWv: 'b',cITimeS: '1740902444',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/search?q=Fractional%20Fourier%20Transform&__cf_chl_f_tk=d2_cPVuUSlh3Jt81b.s6JM9nZtMSlaI31zVosMLAXUg-1740902444-1.0.1.1-6ug2LNrZ367yJO_N9Y7a0QwbFuTKF64xStliFZxcqcc",md: "Rw7Sbzl627P6VLCsKUxF00bpKNHceVI7NfT3TKhnt3c-1740902444-1.2.1.1-zFY2TYz7dTTVOX0khy2SkgpUisI7GHoh9qgQWBmfw3Zn6pHTZjZr4Ql1ucbdIYipSzoT9tRiVybPm129GqTWSiS_dU5UGJb6x1U3mfyIZQJe8041dWnCLIZjua12KcNCW6.f.ap3mv_qx.6Ve7.Z4WAjCiPme.LlxTqhvfVeEP.tZFnJb07rRRUCceCdj.uQgjQ4lbaQ_QVqKqkD1epCrXRmRTBjcx1xo.7bAEFGcq6JRN0.CwB3Kfz.iZyMXYFaYQLH.C1y3i.GZe8OqybQtty29IT3YCDEwu_xvyqIfC_2T6XE9sl6SAmkfUQqPVccvmB5d.qOWkU2Em4I8MfKjNai77hstYqHNWfUIdXSERP3jF_UObnl_X7wk6AvAYGWk9vKrIm7z.mMGcKuWlVUmkRWvpPCGJueYnPQNm44jCjrj44GuU6NWvFN9sijlKB7TxovqI3LE_hvmYj3XWpBYI4J1JvbcsHYW3KdoMVZ8wphjgYMhS6Ub7e82F_ipfGaWo61_fJZG_qrNegQIVATo6lFfohha_Gd.HxsLwVyBGQJHLeYxFF45uvDg6esYbA_Hbs5c0rGQ0y_5pSxNJRjW6O65s3_rUaVOuE6RQ6qV86WjFtAxPuSj0Zb25_J0TrsJvHh_IDot.uqhN5sKmmML_PPNRhavfF8Jk6sZ2L_D5bUXPxeCR2LKnwmExTHU.MAUmjeLBpy5Sbz0xS3BEqvia86zZfPY1x7K2YoeUuezHkzLkvUT9WEHzezhh3LQc2q4VMkNlHRM..Po3DyKF5Hsxwghyh3YUkRAILjquaBedoHNPaWz3DQvE8HgS7GcVuWSaJd271fbWqSmk_ju5gfqzWy4Dyn1ILrgNf8nvP3ib2dy.OfjMGAeQOu7mXaDDAvHhy0iDv7hCZojp_adDuLYlFvblmp8FY7IZcjIWfDLbkWpHlD9Uwa9.FqV5yoY9AXhEymdPsc3lNcEn6F2538H8m9igJpEgA3ItmzF1ijqs_Y0yg84By.VbKhXwIZnBSpaLSKlN4dugHrv1LtiakVcfrAdrl_NtFuRhS8UeEcelrUNLVE.DeVLJYmsBQBJdC4SYv9M7CmmiYSJJ1iNxVJduXATtv3kOTEEAjy2K204sJ6LuCTVePWuSDYFzswIw3ZxN5merL2e6r.ZfjQHwWX1ZzmYbggUu4c0Fw_stkB2g6Zfuvvj9XdpvVqFouWpOM2CIdW_NQyprnBDWzbdy0Z5Frj_G.9vuQWeFRXbQ.p88qRjBFGBr3N93Wh6ztVijrXioDpLYfG6j4QCtzWDnsXiGVL1Crr2poGTXJJlowN5P4",mdrd: ".jYqp6axL13lRDf8rEgMEsQoGfQmCRsm.v1h157kbpQ-1740902444-1.2.1.1-zM6nYBRBlbtEVBzMeyk15zEGvQO3rUKGJcEjewk_pjDev3tDOFRKKL17V_nAOZDznslpma5_qThavd5ZcZ0mu1WQcuR5nbl05wZjI5fS1MM1u3VjYdi.9s1TlFDV6PHw3v.BcAEbkap567O7pevFWfbv4Q_36tj_rhuCLA69GIfdNm.sfeg3lq67A9nAbwap__WxstM6bTzEzc_1uE3zmJGcegqRwIZgyz22Hmu.I21Tw4qkZrhXY0fMQ_oIb9qNTyvB5FGJS.dIieigjuSYx6ff5JFW5WWlSwhOXf9Ori9fDMDMBgjzWt9XyiaDKtR2L_yNvzqDqGGbyy_GFshArmJvuuueXHEc6GDgBxNTr034ae7jQP_Rv0EyD9eWGdKIvanEwhygVRU48mW89v2qmBunL5jSinHwhhKc4QFUOVKzzm4N9aeeZyroP1dZ24Qf0qwwuyaCyIoQfNWOE6JaJAE9C8lt.ruI6g_YoK8GlfgYFGuiNmF3P8ATlfzH_fMoSq5fPxcVVNv.BnCh8wdiky0vqwIolSdfvT7jBSwxbEkY9A0UWt0CXGuDmYYbN7vSiXTcaJ27l.8TqwYmEnctOnt.xCZp9ku0zNT1YQn2Fnq.mqgf2L.EjIEaElMh.CNx6Q01X7gV7kNQvEHV42fDMD36O9rXSiQS70hM1foWG2jkD3GPXtydOniiYKQ_Tt5oDOLSICfswS2AZvrwuR0GgcyeudeY8vPcpVlm9Cs15HibIdybLLR7FG8CAId_GnV8LBH7GB.bUsOK09MGK6HVViM3f7nj3uMpfxrsntsH1FvEuQ6n9CFG4eE4RHUqaLIK23zRQWDGDlk7qhKi8NTrxgD_NWYyp_.qkLdwBPwPbMW3Lg8xsxtdOsH4Wdf9gTV.7DSigXOJnCWHofAKcemVEfPfMJHFgELeQYVT9mL4C1KeWXbqCWxQoGu2kPFusZYijG3cEwncekbiMcT5Ge3lr2ntMXiy9VX9FQWUNB5qKtPAkeN048HuK5ABXTG4BmkkR_Y4qJAP5VeyqIQcUGkM.2veYhJEQdK7oGtAGgCnNz8RbWvKRRJ.PYWF2e3B8z19j7ObYdalrCueB9uWpUBYW.PPPfbPPaeVHX1RVkXJP2.X7Y93ENEeFtr5qbeaAAErCncPeKyC3l6F7_2UIPI6x1v9Qrqp6_22hMlbI_y90J0IqzKtFGp4D.Z4jYa3U6pm4U.Phr6j7RxV3pRz3AGu4W4mnnS0R.PWyeTcAazxnho6LxNpkKJnX7qXrpHI6j069YxD3hTOLxOjiYPsCbwP0KqzlV1.yGJHeaznNRUESO4yQ_k1MKAQ57MV9yvtXyjM7L.qrk8O287FIgVNU2caTUhJ7.P_LY1UoLBhPjPWXv70JBJDTUOzaNPTjG5qnbL1iiOK.udj61yLAoYxfhv8llrCNx2ftRK9KgLDMjkimEB0huaX_n7zRNrkisCFkQzNjbf9t3Otu41UfZjZ3bx5BmYNnN._3CHTiNCw8QR1Em3lsXBgTLwh5T2tr3J9KXM_4rXe7JuXBfZu9l6whICdfOt4EdqTjrZ2Oyf.0DGKJ8Wug1dzIXOPFUQcNImsgrUQz1EY4Mj2B2SVKsmZX_61JkpHhsoWQMa_nqKaBjl8ZIUJFzyBf.joVciAw.JexHgHoeZ9UfnZoJDKyMDoq2W51hW.G_d3Jys5HgolS0RnC9tj_gD4k3zPwaZyHHbLhaE7cQ8igumdfGGrcldn1y90RolJKERktjfk1pUOinyMF.9YqbeWHLYEsY1VlPqRktbku94SGFeFAJsrW1kZnou8fnfTV3nWr1rijCYLqgnFCcAOGr11SD8243FEWw0rcL7saoWW3B8D0WGBy7b3CLQvmKDzH9WC27av_gYkqf_sDafiUa73.dTsFLdC2fEI3BY_Q29CEDCNFqLlFde19nyzeRUT59yf0MrTBmLTklg0NXRjbelJj6kJ7mpwH7QNKccUNDF8avxKFUl7R7N40czu0g"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=919f5cb8dbc8cdfe';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/search?q=Fractional%20Fourier%20Transform&__cf_chl_rt_tk=d2_cPVuUSlh3Jt81b.s6JM9nZtMSlaI31zVosMLAXUg-1740902444-1.0.1.1-6ug2LNrZ367yJO_N9Y7a0QwbFuTKF64xStliFZxcqcc" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>