A sampling expansion for nonbandlimited signals in chromatic derivatives

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.