A Slice of Trispectrum for Patterns of Modulation

Abstract

<p>Modulation can be identified in a signal from correlations of power across frequencies. Resolving power over time and frequency using standard techniques of bandpass filtering and squaring creates bias: filtering presupposes a timescale and bandwidth for modulation, while squaring complicates separation from noise. Higher-order spectra (HOS) can be used to estimate power correlations without bias. HOS are not widely familiar because their meaning is thought to be obscure. A natural interpretation of the fourth-order spectrum (trispectrum) as a measure of linear relationships between power across frequencies is explained. This interpretation motivates a new tool, the modulogram, for identifying various types of modulation. The modulogram can be further decomposed into a low-dimensional feature space describing characteristic patterns of modulation. These developments are demonstrated with the blind identification of beta burst in rodent local field potential (LFP) recordings.</p>