Some fundamental properties of MMSE filter banks

We design filter banks that are best matched to input signal statistics in M-channel subband coders, using a broad class of rate-distortion criteria. We present fundamental properties and analytical expressions for minimum mean-squared error (MMSE) filter banks, without constraints on filter length, under optimal bit allocation requirements. We also investigate a constrained-length version of this problem, which is applicable to practical coding scenarios. While the optimal filter banks are nearly perfect-reconstruction at high rates, we show that MMSE FIR filter banks enjoy a significant advantage (in the MSE sense) over optimal perfect-reconstruction FIR filter banks at all rates.