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A sampling expansion for nonbandlimited signals in chromatic derivatives

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2 Author(s)
G. G. Walter ; Dept. of Math. Sci., Univ. of Wisconsin-Milwaukee, Milwaukee, WI, USA ; Xiaoping Shen

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.

Published in:

IEEE Transactions on Signal Processing  (Volume:53 ,  Issue: 4 )