The Design of Optimum Filters for Quantizing a Class of Non Bandlimited Signals+

We consider the efficient quantization of a class of non bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. By definition, these signals are cwersampled and it is reasonable to expect that we can reap the same benefits of well known efficient A/D conversion techniques. Indeed, by using appropriate multirate reconstruction schemes, we first show that we can obtain a greilt reduction in the quantization noise variance due to the oversampled nature of the signals. To further increase the effective quantizer resolution, noise shaping is introduced by optimizing linear time invariant (LTI) and linear periodically time varying (LPTV)M preand post filters around the quantizer. Closed form expressions for the optimum filters and the minimum mean squared error are derived for each case.