I. Introduction
The classical Wigner distribution (WD) [1] and ambiguity function (AF) [2] are two kinds of important non-stationary signal processing tools and have their own advantages for the detection of linear frequency-modulated (LFM) signals. The former realizes energy accumulation in the time-frequency domain and the latter shows autocorrelation in the time-delay and frequency-shift domain. The WD and AF are defined as \eqalignno{W(t,\omega) &= \int_ {- \infty} ^ {+ \infty} f\left ({t + {\tau \over 2}} \right){f^\ast}\left ({t - {\tau \over 2}} \right){e^ {- j\omega \tau}} {\rm d}\tau &\hbox{(1)}\cr AF(\tau, \omega) &= \int_ {- \infty} ^ {+ \infty} f\left ({t + {\tau \over 2}} \right){f^\ast}\left ({t - {\tau \over 2}} \right){e^ {- j\omega t}}{\rm d}t&\hbox{(2)}}The linear canonical transform (LCT) is also a useful and effective tool for detecting LFM signals, because the LCT of an LFM signal has an energy accumulation property in some specific LCT domains. It is a three free parameter class of linear integral transform [3], which includes the classical Fourier transform (FT), the fractional Fourier transform (FRFT), the Fresnel transform (FST), the Lorentz transform, and the scaling operations as its special cases [4]–[7].