The wavelet transform: a review and application to enhanced data storage reduction in mismatched filter receivers

The wavelet transform (WT) is an efficient time-frequency signal processing tool. In the first part of this paper, a general review of the characteristics of some of the popular time-frequency representations (TFRs) is given. In particular we review the short-time Fourier transform (STFT) and the Wigner distribution (WD). The WT is then reviewed in detail as well as the discrete (orthogonal) wavelet transform (DWT). It is shown that the WT overcomes the main drawbacks of the STFT and the WD w.r.t. simultaneous time and frequency resolution. In the second part of the paper, we present a contribution dealing with a new application of the DWT. In particular, we show that by using orthogonal wavelet basis functions, we achieve a considerable reduction in the data storage needed for the matched receiver of chirp signals. Linear and nonlinear chirp signals with Gaussian envelopes are considered. The simulation results show that with more than 80% reduction, the performance of the matched filter (mismatched in this case) is very close to that of the classical MF receiver without data compression. The results are very important for chirp pulse compression radar systems as well as for digital communication and multiple-access systems based on the use of chirp signals.