Wiener Filter as an Optimal MMSE Interpolator

The ideal sinc filter, ignoring the noise statistics, is often applied for generating an arbitrary sample of a bandlimited signal by using the uniformly sampled data. In this article, an optimal interpolator is proposed; it reaches a minimum mean square error (MMSE) at its output in the presence of noise. The resulting interpolator is thus a Wiener filter, and both the optimal infinite impulse response (IIR) and finite impulse response (FIR) filters are presented. The mean square errors (MSE’s) for the interpolator of different length impulse responses are obtained by computer simulations; it shows that the MSE’s of the proposed interpolators with a reasonable length are improved about 0.4 dB under flat power spectra in noisy environment with signal-to-noise power ratio (SNR) equal 10 dB. As expected, the results also demonstrate the improvements for the MSE’s with various fractional delays of the optimal interpolator against the ideal sinc filter under a fixed length impulse response. Keywords—Interpolator, minimum mean square error, Wiener filter.