The Wigner-Ville Distribution Based on the Offset Linear Canonical Transform Domain

Abstract

Abstract-The Wigner-Ville distribution (WVD) in the offset linear canonical transform (OLCT) domain (WOL) is a tool for signal processing and optics, which has the advantages of the OLCT and good properties of WVD. In this paper, a more simple definition of the WOL is introduced, without changing the instantaneous autocorrelation function to generalization form. Moreover, some new and important properties of the WOL are derived.

The two-dimensional OLCT of angularly periodic functions in polar coordinates

“…As an extension of many other linear transform, the OLCT has a wide range of applications in optics and signal processing. For the OLCT domain signal, people have carried out a lot of promotion, and got a lot of research results on the OLCT convolution, sampling, etc., which can be found in [16][17][18][19][20]. All these results are signals for dealing with one-dimensional (1D) problems.…”

Convolution and correlation theorems for the windowed offset linear canonical transform

“…Definition 1. (OLCT) [1] Let A = (a, b, c, d, u 0 , w 0 ) be a matrix parameter satisfying a, b, c, d, u 0 , w 0 ∈ R, and ad − bc = 1. The OLCT of a signal f (t) ∈ L 2 (R) is defined by…”

“…Hence, without loss of generality, we assume b = 0. If u 0 = 0 and w 0 = 0, the OLCT reduces to the LCT [1], [3], [5], [7].…”

“…The offset linear canonical transform (OLCT) [1], [2], [4], [5], [12], [13] is a generalized version of the linear canonical transform (LCT) with four parameters (a, b, c, d) [6]- [11]. It is a six parameter (a, b, c, d, u 0 , w 0 ) class of linear integral transform.…”

“…Correlation is similar to convolution and it is another useful operation in signal processing, optics and detection applications [20]- [22]. In some domains such as the LCT domain [3], [6], [13], Wignar-Ville transform domain [1], [8], [12] and the OLCT domain [1], [12], the convolution and correlation operations have been studied. They are the most fundamental and important theorems in these domains.…”