All-purpose and plug-in power-law detectors for transient signals

A power-law statistic operating on discrete Fourier transform (DFT) data has emerged as a basis for a remarkably robust detector of transient signals having unknown structure, location, and strength. We offer a number of improvements to Nuttall´s (1994) original power-law detector. Specifically, the power-law detector requires that its data be prenormalized and spectrally white; a constant false-alarm rate (CFAR) and self-whitening version is developed and analyzed. Further, it is noted that transient signals tend to be contiguous both in the temporal and frequency sense, and consequently, new power-law detectors in the frequency and the wavelet domains are given. The resulting detectors offer exceptional performance and are extremely easy to implement. There are no parameters to tune. They may be considered “plug-in” solutions to the transient detection problem and are “all-purpose” in that they make minimal assumptions on the structure of the transient signal, save of some degree of agglomeration of energy in time and/or frequency