Operator theory-based discrete fractional Fourier transform

Date
2019
Advisor
Instructor
Source Title
Signal, Image and Video Processing
Print ISSN
1863-1703
Electronic ISSN
Publisher
Springer
Volume
13
Issue
7
Pages
1461 - 1468
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

The fractional Fourier transform is of importance in several areas of signal processing with many applications including optical signal processing. Deploying it in practical applications requires discrete implementations, and therefore defining a discrete fractional Fourier transform (DFRT) is of considerable interest. We propose an operator theory-based approach to defining the DFRT. By deploying hyperdifferential operators, a DFRT matrix can be defined compatible with the theory of the discrete Fourier transform. The proposed DFRT only uses the ordinary Fourier transform and the coordinate multiplication and differentiation operations. We also propose and compare several alternative discrete definitions of coordinate multiplication and differentiation operations, each of which leads to an alternative DFRT definition. Unitarity and approximation to the continuous transform properties are also investigated in detail. The proposed DFRT is highly accurate in approximating the continuous transform.

Course
Other identifiers
Book Title
Keywords
Fractional Fourier transform (FRT), Operator theory, Discrete transforms, Hyperdifferential operators
Citation
Published Version (Please cite this version)