Synthesis filters design for coding gain in oversampled filter banks

In this letter, we study the impact of the design freedom brought about by oversampling in perfect reconstruction oversampled filter banks, on the choice of synthesis filters that maximize the coding gain. In particular, based on the expression of the coding gain for the oversampled case, we show the dependency of the coding gain on both analysis and synthesis filters. We explore how the choice of synthesis filters can affect the coding gain, given a fixed set of analysis filters. We show that the para-pseudo-inverse is a good choice for the maximization of the coding gain when the corresponding analysis filters have been optimized for coding gain under critical sampling.