THE GENERALIZED EXPONENTIAL TIME-FREQUENCY DISTRIBUTION

Time-frequency distributions (TFD) are joint time and frequency signal representations that, among other properties, maintain the true support of a signal's energy in both time and frequency. In addition to their mathematical elegance, TFD's can provide simultaneous resolution in time and frequency that exceeds that of the common spectrogram. In general, however, TFD's, also exhibit certain peculiarities that arise, in part, from the bilinear structure of the fundamental TFD form (L. Cohen's class). Perhaps most notable is the presence of spectral cross-term artifacts, a kind of spectral chaff that tends to impede visual understanding and interpretation of TFD's as instantaneous power spectrums. Several researchers have proposed and demonstrated a variety of TFD's, which through Cohen's form are defined through a kernel phi(theta, tau). Particularly notable among these is Choi and Williams' exponential distribution in which phi(theta, tau) = exp(-theta2tau2/sigma). Of all distributions investigated, the exponential distribution is relatively immune to spectral cross-term generation and yet maintains high simultaneous time-frequency resolution. In a generalization of Choi and Williams' work, we introduce here the broader class of exponential distributions defined by the kernel exp(-\theta\p\tau\q/sigma) and investigate its properties. In particular, we show that this generalized exponential distribution can exceed the time-frequency resolution performance of the exponential distribution and yet also remain relatively free from spectral cross-term distortion.