On the detection of non-stationary signals in the matched signal transform domain

Abstract

This paper proposes a detector of multi-component non-stationary signals based on the matched signal transform (MST). In the MST domain, a non-stationary signal is localized at its frequency modulation rate with the transform's basis modulation function. The MST can be numerically implemented either as a freestanding discrete version of an integral transform, or for faster computation, as a time resampled version of the original signal followed by a fast Fourier transform. We analyze the noise statistics in the MST domain and derive the analytical forms of the probability density function for both implementations, considering the non-stationary signal embedded in white Gaussian noise. We propose a detector based on the squared magnitude of the MST and show how its detection performances depend on the chosen implementation. All the theoretical derivations are validated through Monte Carlo simulations.