Sampling theorems for signals periodic in the linear canonical transform domain

Multichannel interpolation of nonuniform samples with application to image recovery

“…A generalized trigonometric interpolation was considered in [17] to make a good approximation for non-smooth functions. Recently, the nonuniform sampling theorems for trigonometric polynomials were presented [16,24]. Selva [25] proposed a FFT-based interpolation of nonuniform samples.…”

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

“…It was shown in [6] that a random signal, which is not bandlimited in the Fourier domain, can be approximated by its samples via Shannon sampling theorem. Motivated by [6], in this subsection, we show in a broader sense that a random signal X(t), which is not bandlimited in the LCT domain, can be approximated by its uniform sampling series (29), provided that X(t) satisfies some mild conditions. The following result can be proved similar to [6, Theorem 1].…”

“…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].…”

Uncertainty principles associated with the offset linear canonical transform

“…The offset linear canonical transform (OLCT) [1][2][3][4] is known as a six parameter (a, b, c, d, , ) class of linear integral transform, which is a time-shifted and frequency-modulated version of the linear canonical transform (LCT) with four parameters (a, b, c, d). [5][6][7][8][9][10][11] The two extra parameters, ie, time shifting and frequency modulation , make the OLCT more general and flexible, and thereby the OLCT can apply to most electrical and optical signal systems. It basically says that the Fourier transform (FT), the fractional Fourier transform (FrFT), the Fresnel transform (FnT), the LCT, and many other widely used linear integral transforms in signal processing and optics are all special cases of the OLCT.…”