Interpretation of Time-Frequency Distribution Cross Terms

Noise and vibration signals which are stationary are frequently analyzed for frequency content using Fourier Transform methods. Frequency content can be clearly displayed, but temporal characteristics of signals can easily be obscured in a frequency spectrum. Several commonly available methods of analyzing nonstationary signals are available, such as short-time Fourier Transform and wavelet analysis. Smearing of data in the time and/or frequency domains leads to limited usefulness of these methods in analyzing rapidly varying signals. This also applies to stationary signals with perceivable temporal characteristics.

The Wigner Distribution is a time-frequency analysis which can analyze rapidly varying signals and show the effects of rapid changes in signal characteristics. It is appealing because it fully preserves all the information present in the original signal. However, the Wigner Distribution of a measured signal typically contains cross terms which do not correspond to spectral components in the original signal. Much success has been achieved at reducing cross terms by modifying the Wigner Distribution (at the expense of losing some of the original signal information). The objective of this paper is to show that these cross terms contain information about temporal variations of the signal envelope and are not just artifacts of the Wigner Distribution calculation.