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

Recently, a power-law statistic operating on discrete Fourier transform (DF T) data has emerged as a basis for a remarkably robust detector of transien t signals having unknown structure, location, and strength. In this paper, we offer a number of improvements to Nuttall's original power-law detector. Specifically, the power-law detector requires that its data be prenormaliz ed and spectrally white; a constant false-alarm rate (CFAR) and self-whiten ing version is developed and analyzed. Further, it is noted that transient signals tend to be contiguous both in temporal and frequency senses, and co nsequently, new power-law detectors in the frequency and the wavelet domain s are given. The resulting detectors offer exceptional performance and are extremely easy to implement. There are no parameters to tune. They may be c onsidered "plug-in" solutions to the transient detection problem and are "a ll-purpose" in that they make minimal assumptions on the structure of the t ransient signal, save of some degree of agglomeration of energy in time and /or frequency.