Polynomial-based digital filters as prototype filters in DFT modulated filter banks

In this paper, we investigate the possibility to use polynomial-based digital FIR filters as prototype filters in DFT and cosine modulated filter banks. In order to apply the FIR filter with piecewise polynomial response as prototype filter in the filter bank, it is beneficial to find expressions for polyphase components of the filter. In the paper it is shown that it is possible to construct the two following polyphase decompositions of polynomial-based digital filters for implementation; (i) polyphase decomposition based on the prolonged Farrow structure, and (ii) polyphase decomposition based on the transposed Farrow structure. The paper shows that both polyphase structures have the same multiplication rate, while the polyphase decomposition based on the prolonged Farrow structure has a considerable smaller number of multipliers. Both structures are equivalent in terms of filter performance in the frequency domain, and can be used as prototype filter in DFT and cosine modulated filter bank.