The ambiguity function associated with the linear canonical transform

Abstract

A new kind of ambiguity function (AF) associated with the linearcanonical transform (LCT) is proposed in this article, this new AF is defined based on the LCT and the classical AF. Firstly, the main properties and physical meanings of the newly defined AF are investigated, the results show that this kind of AF can be seen as one generalization of the classical AF. Then, the newly defined AF is applied to detect the parameters of the linear frequency modulated signals by combining with the classical Radon transform. The simulations are performed to verify the correctness of the derived results, and the comparison of the derived results with the common time-frequency analysis tools are also discussed.

Instantaneous frequency estimation based on the linear canonical transform

“…The classical Shannon sampling theory has been generalized to the LCT domain [19,20], the well known convolution and product theorem [21,22], the uncertainty principles [23] and the spectral analysis [12] are well investigated in the LCT domain. Recently, more results are derived and proposed associate with the ambiguity function [24], the Wigner-Ville distribution [25] and the extrapolation method [26] in the linear canonical transform domain. For the best of our knowledge, there are no paper published associated with the IF estimation in the LCT domain, it is therefore interesting and worthwhile to study the IF estimation methods based on the LCT.…”

The short-time Wigner-Ville distribution associated with linear canonical transform

“…The WD in the LCT domain (WDL) is proposed as a generalized WD that is associated with the LCT by replacing the orthogonal kernels of the FT with the non-orthogonal kernels of the LCT. [5][6][7]…”

Various generalizations of uncertainty principles related to the linear canonical ambiguity function

“…The authors of [1,11,16] proposed the windowed linear canonical transform and the uncertainty principles concerning this transform is also demonstrated. The authors of [3,6,8,10] studied the linear canonical ambiguity function, which is a generalization of the ambiguity function in the LCT space. Several essential properties and an application of the generalized transform is also discussed.…”