  The principle of stationary phase (PSP) is re-examined in the context of
linear time-frequency (TF) decomposition using Gaussian, gammatone and
gammachirp filters at uniform, logarithmic and cochlear spacings in frequency.
This necessitates consideration of the use the PSP on non-asymptotic integrals
and leads to the introduction of a test for phase rate dominance. Regions of
the TF plane that pass the test and don't contain stationary phase points
contribute little or nothing to the final output. Analysis values that lie in
these regions can thus be set to zero, i.e. sparsity. In regions of the TF
plane that fail the test or are in the vicinity of stationary phase points,
synthesis is performed in the usual way. A new interpretation of the location
parameters associated with the synthesis filters leads to: (i) a new method for
locating stationary phase points in the TF plane; (ii) a test for phase rate
dominance in that plane. Together this is a TF stationary phase approximation
(TFSFA) for both analysis and synthesis. The stationary phase regions of
several elementary signals are identified theoretically and examples of
reconstruction given. An analysis of the TF phase rate characteristics for the
case of two simultaneous tones predicts and quantifies a form of simultaneous
masking similar to that which characterizes the auditory system.
