Open AccessAlgebraic representation for fractional Fourier transform on one‐dimensional discrete signal models
Author(s) -
Zhang ZhiChao
Publication year - 2018
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
ISSN - 1751-9683
DOI - 10.1049/iet-spr.2017.0217
Subject(s) - fractional fourier transform , discrete time signal , discrete fourier transform (general) , multidimensional signal processing , signal processing , non uniform discrete fourier transform , signal (programming language) , fourier transform , algebraic number , representation (politics) , algorithm , mathematics , sampling (signal processing) , algebra over a field , computer science , mathematical analysis , fourier analysis , analog signal , pure mathematics , digital signal processing , signal transfer function , telecommunications , politics , political science , law , programming language , computer hardware , detector
Algebraic signal processing provides a general framework for studying theoretical problems (sampling, transform domain analysis etc.) in the classical signal processing. In this study, theauthors extend algebraic representation for the conventional Fourier transform (FT) to the fractional FT (FRFT) domain, from which the algebraic structures for the FRFT on infinite and finite one‐dimensional signal models are obtained. They show that FRFTs on the infinite and finite discrete‐time (DT) signal models, respectively, are none other than the DTFRFT and the closed‐form discrete FRFT. They also derive FRFTs on the infinite and finite discrete‐nearest neighbour signal models, and finally they discuss their applications in optical and time–frequency signal processing.