Convolution and Correlation Theorems for Wigner-Ville Distribution Associated with the Quaternion Offset Linear Canonical Transform

09/01/2021
by   Mohammad Younus Bhat, et al.
0

The quaternion offset linear canonical transform(QOLCT) has gained much popularity in recent years because of its applications in many areas, including color image and signal processing. At the same time the applications of Wigner-Ville distribution (WVD) in signal analysis and image processing can not be excluded. In this paper we investigate the Winger-Ville Distribution associated with quaternion offset linear canonical transform (WVD-QOLCT). Firstly, we propose the definition of the WVD-QOLCT, and then several important properties of newly defined WVD-QOLCT, such as nonlinearity, bounded, reconstruction formula, orthogonality relation and Plancherel formula are derived. Secondly a novel canonical convolution operator and a related correlation operator for WVD-QOLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation theorems are studied.We also show that the convolution and correlation theorems of the QWVD and WVD-QLCT can be looked as a special case of our achieved results.

READ FULL TEXT
research
03/24/2022

Uncertainty Principles for the Short-time Free Metaplectic Transform

The free metaplectic transformation (FMT) has gained much popularity in ...
research
12/14/2016

The Mehler-Fock Transform and some Applications in Texture Analysis and Color Processing

Many stochastic processes are defined on special geometrical objects lik...
research
06/03/2017

Discrete Gyrator Transforms: Computational Algorithms and Applications

As an extension of the 2D fractional Fourier transform (FRFT) and a spec...
research
10/19/2019

Robustifying multiple-set linear canonical analysis with S-estimator

We consider a robust version of multiple-set linear canonical analysis o...
research
11/06/2018

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator

By deriving influence functions related to multiple-set linear canonical...
research
06/23/2020

Efficient Spatially Adaptive Convolution and Correlation

Fast methods for convolution and correlation underlie a variety of appli...
research
04/14/2021

Zaionc paradox revisited

Canonical expressions are representative of implicative propositions upt...

Please sign up or login with your details

Forgot password? Click here to reset