Operator (biology)

Orthogonality

Offset (computer science)

Quaternion

Pure mathematics

Mathematics

Convolution (computer science)

Transcription factor

Gene

Algorithm

Signal processing

Artificial intelligence

Repressor

Chemistry

Programming language

Geometry

Computer science

Digital signal processing

Computer hardware

Linear map

Artificial neural network

Biochemistry

Signal Image and Video Processing

The quaternion offset linear canonical transform (QOLCT) has gained much popularity in recent years because of its applications in many areas, including image and signal processing. At the same time, the applications of Wigner–Ville distribution (WVD) in signal analysis and image processing cannot be excluded. In this paper, we investigate the Wigner–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 reconstruction formula, orthogonality relation, are derived. Secondly, a novel canonical convolution operator and a related correlation operator for WVD-QOLCT are proposed. Based on the proposed operators, the corresponding generalized convolution and correlation theorems are studied. Moreover on the application part, detection of the linear frequency modulated signals is established in detail by constructing an example.

Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform