Detection of Long-Duration Narrowband Processes

In this paper we are concerned with the detection of quiet narrowband signals. More specifically, we assume that these signals are: 1) extremely weak, with a signal-to-noise ratio (SNR) of ¡20 dB or below on a per-sample basis, 2) moderately long, of the order of minutes or tens of minutes, and 3) narrowband but not tonal, with, for example, a bandwidth of a few tens of Hz at a sampling rate of a few kHz. Such signals can arise from a variety of acoustic sources, and detecting them is an important problem in signal processing. As regards the assumption that the signal is narrowband, note that this bandwidth is not known, although it can be assumed not to vary with respect to time. Thus a detector “tuned” for a bandwidth of 10 Hz may perform poorly when in truth the bandwidth is 30 Hz. Our goal is to establish a detection structure which can take advantage of a narrowband nature, yet is robust when the bandwidth increases. There are several possible models for the signals of interest. One is that of a harmonic set: