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

Nonuniform sampling for random signals bandlimited in the linear canonical transform domain

“…In particular, when ξ n and ζ n are constants and both are equal to zeros, i.e., the nonuniform sampling studied in this paper reduces to uniform sampling, we have E[|x(t) − x(t)| 2 ] = 0 from Theorem 3.6. Therefore the result of uniform sampling proposed in [10,Theorem 3.4] is a special case of Theorems 3.5 and 3.6 in this paper.…”

“…In [10,7], a model of LCT multiplicative filter has been introduced as in Fig. 1, where X(u) = L A {x(t)}(u), Y (u) = X(u)H(u), and the output function y(t) is given by…”

“…For random signals which are bandlimited in the LCT domain, there exist few results on sampling theorems. In [10], based on the framework of LCT auto-correlation function and power spectral density, we investigated the uniform sampling theorem and multichannel sampling theorem for random signals which are bandlimited in LCT domain. In this paper, we derive the relationship between the LCT auto-power spectral densities of the inputs and outputs.…”

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.…”

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

“…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].…”