Fractional Bi-Spectrum

TL;DR

The paper introduces fractional bispectrum, a new spectral tool that remains nonzero for certain signals where traditional bispectrum is zero, aiding in noise reduction.

Contribution

It proposes the fractional bispectrum, extending bispectrum analysis to better detect signals with specific frequency relationships.

Findings

Fractional bispectrum is nonzero for signals with specific frequency combinations.

It remains zero for Gaussian signals, similar to traditional bispectrum.

It can be used to reduce Gaussian noise in signal processing.

Abstract

A signal with discrete frequency components, has a zero bispectrum if no linear combination of the frequencies equals one of the frequency components. We introduce fractional bispectrum in which for such signals the fractional bispectrum is nonzero. It is shown that fractional bispectrum has the same property as bispectrum for Gaussian signals: the fractional bispectrum of a zero mean Gaussian signal is zero; therefore it can be used to eliminate or reduce the Gaussian noise.