Linear canonical ripplet transform: theory and localization operators

Discrete Octonion Linear Canonical Transform: Definition and Properties

“…The linear canonical transform (LCT) [1][2][3] is a generalized form of the fractional Fourier transform (FrFT). As a linear integral transform with three parameter class, the LCT is more flexible than the FrFT and is a widely used analytical and processing tool in applied mathematics and engineering [4][5][6][7][8]. For analyzing and processing the non-stationary spectrum of finite-duration signals, Pei and Ding [9] proposed the discrete linear canonical transform (DLCT).…”

Spectral Theorems in the Laguerre Hypergroup Setting

“…Recently, the field of time-frequency analysis has attired many researchers. For examples, we note that Ben Hamadi and all have studied the generalized Fourier multipliers in [4] and the uncertainty principles associated with some integral transforms [5,6], Ghobber and all in [17][18][19] have studied the wavelet multipliers in the Bessel setting and the theory of localization for some integral transforms, Lamouchi and all have also studied some problems of time-frequency analysis in [27,28], for the spherical mean operator and for the short time Fourier transform, Mejjaoli in [31][32][33][34] has studied the wavelet multipliers in the Dunkl and the deformed Fourier settings, Sraeib in [44,45] has studied the uncertainty principles in the quantum theory and the applications of the deformed Wigner transform to the Localization operators theory, Tantary and all in [43,46] have studied the localization operators and uncertainty principles for the Ridgelet transformation in the Clifford setting.…”