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

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.