O. Akay et Gf. Boudreaux-bartels, Fractional convolution and correlation via operator methods and an application to detection of linear FM signals, IEEE SIGNAL, 49(5), 2001, pp. 979-993
Using operator theory methods together with our recently introduced unitary
fractional operator, we derive explicit definitions of fractional convolut
ion and correlation operations in a systematic and comprehensive manner. Vi
a operator manipulations, we also provide alternative formulations of those
fractional operations that suggest efficient algorithms for discrete imple
mentation, Through simulation examples, we demonstrate how well the propose
d efficient method approximates the continuous formulation of fractional au
tocorrelation, It is also shown that the proposed fractional autocorrelatio
n corresponds to radial slices of the ambiguity function (AF), We also sugg
est an application of the fast fractional autocorrelation for detection and
parameter estimation of linear FM signals.