Optimal FIR pre- and postfilters for decimation and interpolation of random signals

A technique for the design of finite-impulse-response (FIR) filters for decimation and interpolation in multirate systems is introduced. FIR prefilters and postfilters that jointly minimize a frequency-weighted mean-square error between the original and reconstructed signals can be designed. There is no need for ideal filter prototypes: the optimal pre-postfilter pair is determined from the signal and noise spectra and the up-sampling and down-sampling factors. Some examples of image and speech processing show that the mean square optimal filter pair leads to typical SNR improvements of 2-6 dB, in comparison to other commonly used filters.>