Analysis of Signals via Non-Maximally Decimated Non-Uniform Filter Banks

Abstract

This paper addresses the important problem of reconstructing a signal from multiple multirate observations. The observations are modeled as the output of an analysis bank, and time-domain analysis is carried out to design an optimal FIR synthesis bank. We pose this as a minimizing the mean-square problem and prove that at least one optimal solution is always possible. A parametric form for all optimal solutions is obtained for a non-maximally decimated filter bank. The necessary and sufficient conditions for an optimal solution, that results in perfect reconstruction (PR), are derived as time-domain pseudocirculant conditions. This represents a novel theoretical contribution in multirate filter bank theory. We explore PR in a more general setting. This results in the ability to design a synthesis bank with a particular delay in the reconstruction. Using this delay, one can achieve PR in cases where it might not have been possible otherwise. Further, we extend the design and analysis to nonuniform filter banks and carry out simulations to verify the derived results.

Optimization of Multi-Subband Parallel and Signal Reconstruction for Remote Sensing Satellite Data Transmission

“…Fig. 4 shows the comparison of the proposed optimized filter and the prototype filter designed in [21] and [22]. The passband cutoff frequency, stopband start frequency, and order of the three are consistent.…”

“…The filter optimized in this article reduces the reconstruction error in the subband overlap area on the premise of losing a certain degree of passband flatness. In combination with the comparison of reconstruction error in Table III, compared with the maximum reconstruction error of 0.28 dB in [21] and 0.17 dB in [22], the filter designed in this article can maintain the full-bandwidth reconstruction mean squared error of 0.0001 dB, with the maximum error not exceeding 0.04 dB. It can achieve highamplitude consistency across the entire frequency band.…”

“…The prototype filter optimized and designed in this article meets the constraint conditions. Compared with [21] and [22], it has a greater stopband attenuation and a more pronounced trend of steep descent in the transition zone. It is beneficial for reducing the "bulge" phenomenon in the overlapping zone.…”

“…The filter optimization criteria prioritize ensuring the flatness of the passband and the attenuation of the stopband, with lower weights for the transition band. Patel et al [22] adopt a subband parallel and reconstruction method based on weighted overlapping additive structure filter banks. When designing the prototype filter, the power complementarity characteristic was not included as a strong constraint in the mathematical optimization formula, which can result in significant transition band reconstruction errors.…”

Design of a novel CEM‐FRM‐based low‐complexity channelised radar transmitter

“…The polyphase‐IDFT channelised transmitter structure is an efficient form of the synthesis filter bank structure. The prototype filter is replaced by the polyphase filter and IDFT [22, 23]. The central frequency of the k th sub‐channel is where K is the number of sub‐channels.…”