The Linear Canonical Transform and Its Application to Time-Frequency Signal Analysis

The linear canonical transform (LCT), which is a generalization of the classical Fourier transform and fractional Fourier transform (FRFT), is an important time-frequency analysis tool. It can analyze the signal in between the time and frequency domains. In this paper, we first introduce the LCT and a number of its properties and then discuss the LCT´s relationships with time-frequency representations (TFR´s) such as the Wigner distribution, the ambiguity function, and other quadratic TFR´s. These relationships have a very simple and natural form and show that the LCT performs a homogeneous linear mapping in the time-frequency plane.Finally, an example of the application about the LCT to time-frequency signal filtering is given.