Detecting arcing faults is an important but difficult-to-solve practical problem. Many existing methods of arc detection are based upon acquiring a signal that is proportional to current and then making an analysis of the signal's power spectrum (or, equivalently, its covariance function). Since the power spectrum, i.e., the absolute values of the Fourier transform, carries only partial information about the signal, a natural question is: why should we restrict ourselves to the use of this partial information? A related question is caused by the fact that even the most efficient methods still miss some arcing faults and/or lead to false detection; what methods should we use to improve the quality of arc detection?
Our analysis is much more general than the arc detection problem and can be used to justify and select detection methods in other applied problems as well.