Linear fractionally invariant systems: fractional filtering and correlation via fractional operators

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.