Study of the Applicationas of Discrete Linear Chirp Transform

Abstract

The discrete Fourier transform (DFT) plays a significant role in analyzing characteristics of stationary signals in the frequency domain in signal processing. The DFT can be implemented in a very efficient way using the fast Fourier transform (FFT) algorithm. However, many actual signals by their nature are non-stationary signals which make the choice of the DFT to deal with such signals not appropriate. Alternative tools for analyzing non-stationary signals come with the development of time-frequency distributions (TFD). The Wigner-Ville distribution is a time-frequency distribution that represents linear chirps in an ideal way, but it suffers from the problem of cross-terms which makes the analysis of such tools unacceptable for multi-component signals. Consequentially, for the analysis of the chirp signal Fractional Fourier Transform (FrFT) has been reported. The FrFT converts a chirp signal from time domain to another domain corresponding to fractional order α. It provides us with an additional degree of freedom (order of the transform α). Later the DLCT is discussed in the literature which is not a time- frequency transform but rather a frequency chirp-rate transform. It converts a non-sparse signal into sparse one using its property of modulation and duality.