Periodic Gabor Functions with Biorthogonal Exchange: A Highly Accurate and Efficient Method for Signal Compression

摘要

We propose a new formalism for signal compression based on the Gabor basisset. By convolving the conventional Gabor functions with Dirichlet functions weobtain a periodic version of the Gabor basis set (pg). The pg basis is exactfor functions that are band-limited with finite support, bypassing theBalian-Low theorem. The calculation of the pg coefficients is trivial andnumerically stable, but the representation does not allow compression. However,by exchanging the pg basis with its biorthogonal basis and using the localizedpg basis to calculate the coefficients, large compression factors are achieved.We illustrate the method on three examples: a rectangular pulse, an audiosignal and a benchmark example from image processing.