Multichannel Sampling of Signals Band-Limited in Offset Linear Canonical Transform Domains

A generalized convolution theorem for the special affine Fourier transform and its application to filtering

“…Simultaneously, as the generalization of FT, the relevant theory of SAFT has been developed including the convolution theorem, uncertainty principle, sampling theory and so on [16][17][18], which are generalizations of the corresponding properties of the FT, FRFT and LCT [3,9,[19][20][21][22][23][24][25][26][27][28]. Conventional convolution operations for FT are fundamental in the theory of linear timeinvariant (LTI) system [9].…”

“…Recently, along with applications of the LCT in the signal processing community [5,9,[11][12][13][14][15], the role of the SAFT for signal processing has also been noticed. It has found many applications in optics, signal processing, and many other applications [3,4,[16][17][18].…”

Sampling theorems and error estimates for random signals in the linear canonical transform domain

“…Sampling is fundamental and significant in signal processing and communications because it provides a bridge between continuous and discrete signals. Sampling theorems for a deterministic signal bandlimited in the LCT domain have been extensively studied in the literature [11,18,22,26,[28][29][30][31]. In the real world, however, some random character is inherent in physical signals, and thus, it is much more convenient to model processes as random signals in many practical situations [1,9].…”

Poisson Summation Formulae Associated with the Special Affine Fourier Transform and Offset Hilbert Transform

“…In addition, the generalized Hilbert transform closely related to SAFT, called offset Hilbert transform (OHT), is another powerful tool in the fields of optics and signal processing community [15]. It has been presented recently and widely used for image processing, especially for edge detection and enhancement, because it can emphasize the derivatives of the image [16,17].…”

“…It has been presented recently and widely used for image processing, especially for edge detection and enhancement, because it can emphasize the derivatives of the image [16,17]. In recent decades, many essential theories and useful applications of SAFT and OHT have been derived from in-depth researching on it [8,15,18,19].…”