A discrete linear chirp transform (DLCT) for data compression

Abstract

Compressive sensing attempts to simplify the frequency transformation and thresholding steps, commonly done in data compression, into one. Sparseness of the signal, in either time or frequency, is required for the convex optimization in compressive sensing to perform well. Although sparseness of certain signals, in either time or frequency, is guaranteed by the uncertainty principle signals composed of chirps are not however sparse in either domain. In this paper we propose an orthogonal linear-chirp transform, the discrete linear chirp transform (DLCT), to represent any signal in terms of linear chirps, with modulation and dual properties. Using the DLCT the sparseness of the signal in either time or frequency can be assessed, and if not sparse in neither of these domains, the modulation and dual properties of the DLCT provide a way to transform the signal into a sparse signal. The application of the proposed DLCT is in data compression. The transformation is illustrated by using sparse and not sparse test signals as well as actual signals.