Auto-term representation by the reduced interference distributions: a procedure for kernel design

Abstract

An analysis of auto-term presentation using the reduced interference distributions (RID) is done. Comparison with an ideal time-frequency signal representation is taken as a basis for this analysis. The following distributions are considered: Choi-Williams (1989), Zao-Atlas-Marks, Born-Jordan, sinc, Zhang-Sato (see ibid., vol.42, no.1, p.54, 1994), Butterworth, spectrogram, and the author's recently proposed S-method for time-frequency analysis. Various distributions produce different auto-term shapes. In all cases, the condition for cross-term reduction is contradictory to the condition for high auto-term quality. A procedure for designing a kernel that will produce the desired auto-term shape is demonstrated. An optimal kernel, with respect to the auto-term quality and cross-term suppression, is derived.