New Integral Transforms for Generalizing the Wigner Distribution and Ambiguity Function

Sampling theorem for the short-time linear canonical transform and its applications

“…The linear canonical transform (LCT) is a three free parameter class of linear integral transform [9][10][11][12][13][14]. It was proposed in 1970s [9,10] and includes the FT, the fractional Fourier transform (FRFT), the Fresnel transform (FST), and the scaling operations as its special cases [11][12][13][14].…”

“…It was proposed in 1970s [9,10] and includes the FT, the fractional Fourier transform (FRFT), the Fresnel transform (FST), and the scaling operations as its special cases [11][12][13][14]. The LCT has found many applications in optics, signal and image processing, and pattern recognition [11][12][13].…”

Computation of the Short-Time Linear Canonical Transform with Dual Window

“…When we select Gaussian window, the STFT becomes the Gabor transform (GT). In recent years, with the development of nonstationary signal processing technology, the linear canonical transform (LCT) was developed by many scholars [2][3][4][5][6][7][8][9]. It is a generalized form of the FT and the Fractional Fourier transform (FRFT) and has been considered to be a powerful analyzing tool in signal processing and optics [10][11][12][13][14][15].…”

New convolution structure for the linear canonical transform and its application in filter design

“…Then, it was applied to the analysis of the optical systems in the early years [5,6,[13][14][15]. With in-depth research on the LCT, it has found many applications in some others fields, such as radar and sonar systems analysis, pattern recognition, time-frequency analysis, and image watermarking [3,4,[16][17][18][19][20][21]. Particularly, the LCT is very useful and effective in non-stationary signal processing since it can be regarded as the decomposition of a signal based on a non-orthogonal basis [18][19][20][21].…”

“…With in-depth research on the LCT, it has found many applications in some others fields, such as radar and sonar systems analysis, pattern recognition, time-frequency analysis, and image watermarking [3,4,[16][17][18][19][20][21]. Particularly, the LCT is very useful and effective in non-stationary signal processing since it can be regarded as the decomposition of a signal based on a non-orthogonal basis [18][19][20][21]. Meanwhile, some fundamental theories and concepts associated with the LCT have been established, for example the convolution and product theorems [22][23][24][25][26][27][28], the uniform and nonuniform sampling theorems [29][30][31][32][33][34], and the uncertainty principles [35][36][37][38][39].…”