{"title":"Wiener Filter as an Optimal MMSE Interpolator","authors":"Tsai-Sheng Kao","volume":6,"journal":"International Journal of Electronics and Communication Engineering","pagesStart":950,"pagesEnd":953,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/14174","abstract":"The ideal sinc filter, ignoring the noise statistics, is often\r\napplied for generating an arbitrary sample of a bandlimited signal by\r\nusing the uniformly sampled data. In this article, an optimal interpolator is proposed; it reaches a minimum mean square error (MMSE)\r\nat its output in the presence of noise. The resulting interpolator is\r\nthus a Wiener filter, and both the optimal infinite impulse response\r\n(IIR) and finite impulse response (FIR) filters are presented. The\r\nmean square errors (MSE-s) for the interpolator of different length\r\nimpulse responses are obtained by computer simulations; it shows that\r\nthe MSE-s of the proposed interpolators with a reasonable length are\r\nimproved about 0.4 dB under flat power spectra in noisy environment with signal-to-noise power ratio (SNR) equal 10 dB. As expected,\r\nthe results also demonstrate the improvements for the MSE-s with various fractional delays of the optimal interpolator against the ideal\r\nsinc filter under a fixed length impulse response.","references":"[1] Oppenheim, A. V. and Schafer, R. W., Digital Signal Processing, Prentice-Hall, NJ, 1989.\r\n[2] Laakso, T. I., Valimaki, V., Karjalainen, M., and Laine, U. K.,\"Splitting the unit delay: tools for delay filter design,\" IEEE Communication Magizine, vol. 13, issue 1, pp. 30-60. Jan. 1999.\r\n[3] Gardner, F. M., \"Interpolation in digital modems-part I: fundamentals,\"\r\nIEEE Trans. Commun., vol. 41, no. 3, pp. 501-507, Mar. 1993.\r\n[4] Erup, L., Gardner, F. M., and Harris, R. A., \"Interpolation in digital\r\nmodems-part II: implementation and performance,\" IEEE Trans. Commun.,\r\nvol. 41, no. 6, pp. 998-1008, June 1993.\r\n[5] Makundi, M. and Laakso, T. I. \"Efficient symbol synchronization techniques\r\nusing variable FIR or IIR interpolation filters,\" in Proc. IEEE\r\nISCAS-03, Bangkok, Thailand, Vol. 3, pp. 570-573, May, 2003.\r\n[6] Tseng, C. C., \"Closed-form design of digital IIR integrators using\r\nnumerical integration rules and fractional sample delays\", IEEE Trans.\r\nCircuits and Systems-I, Vol. 54, pp. 643-655, Mar. 2007.\r\n[7] Lu, W. S. and Deng, T. B.,\"An improved weighted least-squares design\r\nfor variable fractional delay FIR filters,\" IEEE Trans. Circuits Systems-II,\r\nvol. 46, pp. 1035-1040, Aug. 1999.\r\n[8] Cain, G. D., Murphy, N. P. and Tarczynski, A., \"Evaluation of several\r\nvariable FIR fractional-sample delay filters\", Proc. IEEE Int. Conf. on\r\nAcoustics, Speech & Signal Processing, Adelaide, vol. 3, pp. 621-624,\r\nApr. 1994.\r\n[9] Bertsekas, D. G., Dynamic programming: deterministic and stochastic\r\nmodels, Englewood Cliffs, New Jersey, 1987.\r\n[10] Hayes, M. H., Statistical digital signal processing and modeling, Wiley,\r\n1996.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 6, 2007"}