Generic Feasibility of Perfect Reconstruction With Short FIR Filters in Multichannel Systems

DOI10.1109/TSP.2011.2166550zbMATH Open1393.94877arXiv1103.0875OpenAlexW2109013725MaRDI QIDQ4573358

Publication date: 18 July 2018

Published in: IEEE Transactions on Signal Processing (Search for Journal in Brave)

Abstract: We study the feasibility of short finite impulse response (FIR) synthesis for perfect reconstruction (PR) in generic FIR filter banks. Among all PR synthesis banks, we focus on the one with the minimum filter length. For filter banks with oversampling factors of at least two, we provide prescriptions for the shortest filter length of the synthesis bank that would guarantee PR almost surely. The prescribed length is as short or shorter than the analysis filters and has an approximate inverse relationship with the oversampling factor. Our results are in form of necessary and sufficient statements that hold generically, hence only fail for elaborately-designed nongeneric examples. We provide extensive numerical verification of the theoretical results and demonstrate that the gap between the derived filter length prescriptions and the true minimum is small. The results have potential applications in synthesis FB design problems, where the analysis bank is given, and for analysis of fundamental limitations in blind signals reconstruction from data collected by unknown subsampled multi-channel systems.

Full work available at URL: https://arxiv.org/abs/1103.0875

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Channel models (including quantum) in information and communication theory (94A40)