A sampling expansion for nonbandlimited signals in chromatic derivatives

Authors:
G.G. Walter;Xiaoping Shen
Affiliations:
Dept. of Math. Sci., Univ. of Wisconsin-Milwaukee, Milwaukee, WI, USA;-
Venue:
IEEE Transactions on Signal Processing
Year:
2005

Citing 0
Cited 3

Chromatic derivatives and local approximations

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New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms

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Generalizations of chromatic derivatives and series expansions

IEEE Transactions on Signal Processing

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Abstract

In this paper, we construct infinite-band filterbanks for perfect reconstruction (PR) using Hermite polynomials and Hermite functions. The analysis filters are linear combinations of derivative operators based on these polynomials-the so-called chromatic derivative filters. Together with the synthesis filterbanks, they give PR for a large class of signals that may have infinite bandwidth. Several other related filterbanks are discussed as well. The error in reconstruction for finite-channel chromatic derivative filterbanks is calculated. Examples are given to demonstrate the use of these chromatic filterbanks.