Localized kernel method for separation of linear chirps

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.