Coprime DFT filter bank design: Theoretical bounds and guarantees

Coprime DFT filter banks (coprime DFTFB) achieve the effect of an MN-DFTFB by using two DFTFBs of size only M and N, where M and N are coprime integers. However, coprime DFTFBs need to be designed properly, to avoid unwanted bumps in stopbands or unsatisfactory total spectrum coverage, quantified by overall amplitude responses. In this paper, a detailed theoretical analysis will be made on the tradeoffs between bumps and overall amplitude responses. It will be shown that the bump level at the center frequency f_b of a bump, is approximately one-fourth of the overall amplitude response at f_b. Then, a novel design will be introduced based on an optimization problem pertaining to overall amplitude responses. The original problem is relaxed to a computationally tractable optimization program, which can be solved with alternating minimization algorithms. It is verified with simulations that the new designs cover the spectrum completely.