Signal transforms for the detection and identification of signals

In this paper the authors address the problem of detection and identification of signals buried in high level noise. Frequency domain techniques with long integration intervals are particularly well suited to perform this task if the signal is composed of a mixture of stationary sinusoidal terms. One can achieve reliable detection even in the very low SNR case. However when the signal itself exhibits time-varying features, even when these are known in advance, detection and identification is reliable only over time intervals where the signal is approximately stationary. The limited integration time puts a lower bound to the allowable SNR. In this paper we propose the use of an adaptive signal transformation previously introduced by the authors, which reverts the time-varying signal to a simpler stationary one. Constant features over time allow longer integration times — up to the duration of the total event — thus granting proper detection even in the extremely low SNR case. This is for example the case of a simple monochromatic or narrow-band signal, whose frequency varies over time, with a known frequency law over time, such as a chirp signal. In the paper we review the relevant features of the proposed transformation and detail our method providing significant bounds for its numerical performance and examples.