Statistical trade-offs in modern time-frequency kernel design

In random processes, reduced spectrum estimate variance becomes an important property which augments the list of desired time-frequency properties of modern distributions. 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 Nyquist interval of the spectrum estimate of a white noise process is used as the measure to be minimized. It is proved that the Born-Jordan kernel has the lowest possible average variance. It is also shown that the cone-shape of the modern time-frequency kernels is primarily responsible for their high variance. A comparison of the statistical performance of different shapes of kernels is provided