A comparison between the modified spectrogram and the pseudo-Wigner-Ville distribution with and without modification

Abstract

Two main factors have previously favoured the choice of the pseudo-Wigner-Ville distribution (PWVD) over the spectrogram for time-frequency analysis of monocomponent signals. First, the PWVD has better resolution, and secondly, it provides a more accurate estimate of the instantaneous frequency. However, Kodera's modification of the spectrogram provides significant improvements in both these areas. The spectrogram's energy can be repositioned closer to the instantaneous frequency, and the spread in time and frequency due to the lag window can be reduced. This paper applies Kodera's modification to the PWVD and demonstrates that the modified PWVD can reduce the small amount of spreading in frequency introduced by the PWVD's time lag window. The performance of the PWVD, the modified spectrogram, and the modified PWVD are compared using time-frequency plots, for a selection of noise-free monocomponent and multicomponent signals. The modified distributions are shown to produce more highly resolved estimates of the instantaneous frequency for the monocomponent signals. The modified spectrogram is particularly useful for multicomponent signals with components that are well separated in time and frequency as it can provide highly resolved individual components without the significant cross terms which are a feature of PWVD.