Title :
Linear fractionally invariant systems: fractional filtering and correlation via fractional operators
Author :
Akay, Olcay ; Boudreaux-Bartels, G. Faye
Author_Institution :
Dept. of Electr. Eng., Rhode Island Univ., Kingston, RI, USA
Abstract :
Using fractional operators, we formulate linear fractionally invariant systems as a generalization of linear time invariant and linear frequency invariant systems. We give explicit expressions for convolution and correlation operations for fractional domains and investigate some of their properties. We also provide alternative formulations of fractional convolution and correlation in terms of the fractional Fourier transform (FRFT) and conventional time-domain convolution and correlation. We define fractional autocorrelation and state its relation with the narrowband ambiguity function.
Keywords :
Fourier transforms; convolution; correlation theory; filtering theory; frequency-domain analysis; linear systems; mathematical operators; signal processing; time-domain analysis; FRFT; correlation; fractional Fourier transform; fractional autocorrelation; fractional domains; fractional filtering; fractional operators; linear fractionally invariant systems; linear frequency invariant systems; linear time invariant systems; narrowband ambiguity function; time-domain convolution; Autocorrelation; Chirp; Convolution; Filtering; Fourier transforms; Narrowband; Nonlinear filters; Time domain analysis; Time frequency analysis; Time measurement;
Conference_Titel :
Signals, Systems & Computers, 1997. Conference Record of the Thirty-First Asilomar Conference on
Conference_Location :
Pacific Grove, CA, USA
Print_ISBN :
0-8186-8316-3
DOI :
10.1109/ACSSC.1997.679153