%0 Villanova Faculty Authorship
%A Hearon, Steven.
%E Amin, Moeness.
%D 1991
%G English
%T Statistical trade-offs in modern time-frequency kernel design.
%U http://ezproxy.villanova.edu/login?url=https://digital.library.villanova.edu/Item/vudl:173669
%X When dealing with random processes, reduced spectrum estimate variance becomes an important property which augments the list of desired time-frequency properties of modern distributions. In this paper, the degrees of freedom left in the two-dimensional kernel after satisfying the support, the marginal, and the instantaneous frequency requirements are used to yield a kernel of minimum variance. The average variance over the Nyguist interval of the spectrum estimate of a white noise process is used as the measure to be minimized. We prove that the Born-Jordan kernel [1] has the lowest possible average variance. It is also shown that the cone-shape of the modern t-f kernels is primarily responsible for their high variance. A comparison of the statistical performance of different shapes of kernels is provided.