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.