Fundamentals of Signal Processing within the Framework of Subband Representations
DOI:
https://doi.org/10.52575/2687-0932-2025-52-1-145-155Keywords:
signal processing, subband representations, mathematical foundations, digital filtering, lossy compressionAbstract
In this work, the arsenal of mathematical apparatus of digital signal processing based on subband representations is expanded, established on the concept of a part of the signal energy falling into a given subband. Subband representations are of significant importance in the problems of developing digital methods of frequency filtering, lossy compression of audio signals and images, procedures for analyzing and synthesizing signals during information transmission. The authors formulate criteria for optimizing solutions to a number of subband signal processing problems and obtain corresponding computational relationships. It is shown that a number of meaningful signal processing problems can be effectively solved based on subband representations. To solve many meaningful signal processing problems, it is proposed to use a mathematical apparatus based on orthonormal bases of eigenvectors of subband matrices. Examples of specific problems of signal processing based on subband representations are considered, such as optimal linear subband filtering of signals, subband compression of signals with losses, estimation of subband proximity of two signals based on a subband measure, and matching of signals based on a subband similarity measure.
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