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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.