Time-frequency distribution kernel design over a discrete powers-of-two space

Abstract

Abstruct-We introduce a new class of powers-of-two (PFT) kernels for fast real-time implementations of time-frequency (t-f) distributions. In this class, the local autocorrelation function is computed using a series of shifting and addition operations. PFT filter design techniques can be applied to produce fixed kernels or to design data-dependent kernels suitable for specific operating environments. In the t-f context, where the task is to identify the signal autoterms in the t-f domain, a discretized PFT kernel shows little or no difference in performance from its infinite precision counterpart.

Subspace analysis of spatial time-frequency distribution matrices

“…For convenience of analysis, we select those t-f points of constant distribution value for each source signal. In the case where the STFD matrices are averaged over the t-f signatures of sources, i.e., a total of t-f points, the result is given by (21) where is the instantaneous frequency of the th signal at the th time sample.…”

“…Recently, kernels have been devised, specifically tailored to very fast computation, with the binomial kernel devised by Jeong and Williams being the prime example [17]. Methods for decomposition of kernels, leading to fast computation and increased understanding, have also been carried out by White [18], Amin [19], [20], Venkatesan and Amin [21], and Cunningham and Williams [22].…”