Improved frequency marginal estimates for time-frequency distributions

Time-frequency distributions (TFDs) are used for representing the energy density of a signal simultaneously in time and frequency. The frequency marginal is defined as the density of frequency at a particular time. When the frequency marginal is satisfied, it is given by the classical periodogram formulation. In spectral estimation literature, the periodogram is not considered to be a good spectral estimate because of the high variance it exhibits. For this reason, several modified periodogram methods including Thomson's spectral estimation method [1] have been introduced. In tl,is paper, a new kernel design method to obtain a smoothed spectrum as the frequency marginal is introduced. The necessary conditions on the time-frequency kernel are derived. The consequences of this new kernel design method in signal analysis are illustrated with examples.