Joint fractional signal representations

Using the recently introduced Hermitian fractional operator within the char acteristic function operator method, we derive joint fractional representat ions (JFRs) of signals. JFRs are functions of fractional variables defined by the fractional Fourier transform (FRFT). The JFRs generalize the convent ional time-frequency representations in the same manner as the FRFT general izes the conventional Fourier transform. We derive the fractional counterpa rts of the well-known time-frequency analysis tools such as the ambiguity f unction (AF) and the Wigner distribution (WD) and present some of their pro perties. We also analytically compute the fractional AF and the fractional WD of some simple functions and provide plots for a Gaussian amplitude-modu lated chirp (linear FM) and a rectangular function. (C) 2000 The Franklin I nstitute. Published by Elsevier Science Ltd. All rights reserved.