Multi-component power and frequency estimation for a discrete TFD

In a previous article of Pielemeier and Wakefield (see Proc. of IEEE Symposium on Time-Frequency and Time-Scale Analysis, Oct. 4-6, p.421-424, 1992) a discrete time-frequency distribution (TFD) in Cohen´s class was developed for multicomponent musical signals. This TFD´s separable kernel employs low pass filtering in time to achieve limited superposition between components, and either constant-bandwidth or constant-Q smoothing in frequency. We develop instantaneous power and frequency estimators for the components analyzed by this TFD. In the literature, frequency estimators for discrete distributions often compute frequency based on discrete finite phase differences using periodic statistics. We instead start with the underlying continuous analog signal, and using linear statistics, show that estimates from the discrete distribution can be made arbitrarily accurate for the single component cast, while for the multicomponent case, the estimates are minimally biased by time smoothing. Results are demonstrated showing much less bias than common spectrogram estimators. Multicomponent examples include signals which are inharmonic and contain widely varying levels, and AM and FM signals