Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 49, Issue 5, Pages 979-993Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/78.917802
Keywords
Hermitian and unitary fractional operators; Fourier transform; fractional autocorrelation; fractional convolution; fractional Fourier transform; time-frequency analysis
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Using operator theory methods together with our recently introduced unitary fractional operator, we derive explicit definitions of fractional convolution and correlation operations in a systematic and comprehensive manner. Via operator manipulations, we also provide alternative formulations of those fractional operations that suggest efficient algorithms for discrete implementation, Through simulation examples, we demonstrate how well the proposed efficient method approximates the continuous formulation of fractional autocorrelation, It is also shown that the proposed fractional autocorrelation corresponds to radial slices of the ambiguity function (AF), We also suggest an application of the fast fractional autocorrelation for detection and parameter estimation of linear FM signals.
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