Ii. Optimization of the Pre-or Postfilter

A new technique for the design of finite impulse response (FIR) filters for decimation and interpolation in multi rate systems is presented. With this technique, FIR preand postfilters that jointly minimize a frequency-weighted mean-square (MS) error between the original and reconstructed signals can be designed. Unlike most other FIR filter design methods, there is no need for ideal filter prototypes: the optimal pre-postfilter pair is determined from the signal and noise spectra and the upand down-sampling factors. Some examples of image and speech processing show that the MS-optimal filter pair leads to typical SNR improvements of 2-6 dB, in comparison to other commonly used filters. FIR FIR PRE-FIL TER DOWN UP POST.fIL TER