Fractional convolution and correlation via operator methods and an application to detection of linear FM signals

Using operator theory methods together with our previously 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 tho...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2001-05, Vol.49 (5), p.979-993
Main Authors: Akay, O., Boudreaux-Bartels, G.F.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Approximation
Autocorrelation
Computer simulation
Convolution
Correlation
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Formulations
Fourier transforms
Frequency domain analysis
Information, signal and communications theory
Operators
Optical signal processing
Parameter estimation
Signal analysis
Signal and communications theory
Signal mapping
Signal processing
Signal processing algorithms
Signal, noise
Telecommunications and information theory
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Summary:Using operator theory methods together with our previously 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.
ISSN:1053-587X
1941-0476
DOI:10.1109/78.917802