Analysis of the Wigner-Ville transform of periodic signals

In this paper the Wigner-Ville transform of a periodic signal is theoretically analyzed, and reduced to a closed-form expression in terms of the Fourier series coefficients and the fundamental frequency. This result indicates that the Wigner-Ville transform of a periodic signal consists of only discrete frequencies that are related to the fundamental frequency. The instantaneous power, however, at these discrete frequencies varies with time. The result may be expressed as the sum of principle terms which are not time-varying, and time-varying terms. With these designations, it is noted that the principle terms, except for a scaling factor, are equal to the conventional power spectral density of the analytic signal. Experimental results illustrate the theory, and suggest insights that the analysis provides when applied to the sinusoidally modulated FM case