Detecting stationary phase points in the time-frequency plane

This paper describes and supplements a recent re-examination of linear time-frequency decomposition wherein the principle of stationary phase is applied to the synthesis integral. An inherent part of this time-frequency stationary phase approximation (TFSPA) is a test for the stationary phase condition itself. After outlining the development of the TFSPA, the main contribution of this paper is an analysis of the test from the perspective of classical detection theory. This leads to closed form approximations that; (i) quantify performance in terms of false alarm and detection probabilities; (ii) enable the development of improved tests.