The linear canonical transform (LCT) describes the effect of any quadratic phase system (QPS) on an input optical wave field. Special cases of the LCT include the fractional Fourier transform (FRT), the Fourier transform (FT), and the Fresnel transform (FST) describing free-space propagation. Currently there are numerous efficient algorithms used (for purposes of numerical simulation in the are...

The linear canonical transform may be used to simulate the effect of paraxial optical systems on wave fields. Using a recent definition of the discrete linear canonical transform, phase space diagram analyses of the sampling requirements of the direct method of calculating the Fresnel and other linear canonical transforms are more favorable than previously thought. Thus the direct method of cal...

This study aims to achieve an efficient time-frequency representation of higher-dimensional signals by introducing the notion a non-separable linear canonical wavelet transform in L2(Rn). The preliminary analysis encompasses derivation fundamental properties novel integral including orthogonality relation, inversion formula, and range theorem. To extend scope study, we formulate several uncerta...

Quaternion-valued signals along with quaternion Fourier transforms (QFT) provide an effective framework for vector-valued signal and image processing. However, the sampling theory of quaternion valued signals has not been well developed. In this paper, we present the generalized sampling expansions associated with QFT by using the generalized translation and convolution. We show that a σ-bandli...

The linear canonical transform is shown to be one of the most powerful tools for nonstationary signal processing. Based on the properties of the linear canonical transform and the classical Wigner-Ville transform, this paper investigates theWigner-Ville distribution in the linear canonical transform domain. Firstly, unlike the classical Wigner-Ville transform, a new definition of WignerVille di...

The linear canonical transform (the LCT) is a useful tool for optical system analysis and signal processing. It is parameterized by a 2 2 matrix . Many operations, such as the Fourier transform (FT), fractional Fourier transform (FRFT), Fresnel transform, and scaling operations are all the special cases of the LCT. In this paper, we will discuss the eigenfunctions of the LCT. The eigenfunctions...