Statistical trade-offs in modern time-frequency kernel design.
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  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.
|Main Author:||Hearon, Steven.|
|Other Authors:||Amin, Moeness.|