Optimum quantization of a class of non-bandlimited signals

We consider the quantization of a special class of non-bandlimited signals, namely the class of discrete time signals that can be recovered from their decimated version. Similar to sigma-delta modulation ideas, we show that we can obtain a great reduction in the quantization noise variance due to the oversampled nature of these signals. We then consider noise shaping by optimizing a pre- and post-filter around the quantizer and develop a closed form expression for the coding gain of the scheme under study. The use of an orthonormal filter bank as a sophisticated quantizer is investigated and several examples are provided.