Localized kernel method for separation of linear chirps

TL;DR

This paper enhances a signal separation method to effectively isolate chirp signals with low SNR, discontinuities, and crossover points, supported by theoretical analysis and numerical experiments.

Contribution

It modifies and amplifies the Signal Separation Operator (SSO) for better separation of complex chirp signals under challenging conditions.

Findings

Theoretical analysis links minimal separation, amplitude, SNR, and sampling frequency.

Method successfully separates signals with low SNR and discontinuities.

Numerical results demonstrate effectiveness on simulated data with 7 signals.

Abstract

The task of separating a superposition of signals into its individual components is a common challenge encountered in various signal processing applications, especially in domains such as audio and radar signals. A previous paper by Chui and Mhaskar proposes a method called Signal Separation Operator (SSO) to find the instantaneous frequencies and amplitudes of such superpositions where both of these change continuously and slowly over time. In this paper, we amplify and modify this method in order to separate chirp signals in the presence of crossovers, a very low SNR, and discontinuities. We give a theoretical analysis of the behavior of SSO in the presence of noise to examine the relationship between the minimal separation, minimal amplitude, SNR, and sampling frequency. Our method is illustrated with a few examples, and numerical results are reported on a simulated dataset comprising 7 simulated signals.