Use of the trans-spectral-coherence technique to separate signals from noise

Abstract

A new technique to separate signals from noise is proposed. This technique is specifically meant for signals that are wholly or partly generated through some nonlinear process. A signal processing technique is described, which is specifically aimed at such signals. As long as the underlying process can be assumed to be nonlinear, this technique can be beneficially used, even if the details of the generating mechanism are unknown. To accomplish this goal, three new concepts have been introduced. The first is the concept of the transphase. This is a generalization of the concept of phase, except that it applies to two different frequencies. The second concept is that of the trans-spectral coherence (TSC). This is the generalization of the concept of ordinary coherence and is once again valid for two signals at different frequencies. The third concept is that of the auto-trans-spectral coherence (ATSC), which applies to two signals that are duplicate copies of the same signal. It has been shown that these concepts can be used to detect the presence of minute signals (of a nonlinear origin) even when they are mixed with a random noise that exceeds the signal in magnitude. It is shown with a simulated signal that the presence of a signal could be detected when the ratio of signal amplitude to the standard deviation of the noise was 0.1.