Coprime DFT filter bank design: Theoretical bounds and guarantees
Chun-Lin Liu, P. P. Vaidyanathan
Abstract
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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> of a bump, is approximately one-fourth of the overall amplitude response at f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> . 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.
BibTeX
@inproceedings{icassp2015_coprimedftfilter,
title = {Coprime DFT filter bank design: Theoretical bounds and guarantees},
author = {Chun-Lin Liu and P. P. Vaidyanathan},
booktitle = {ICASSP 2015},
year = {2015}
}