Special purpose correlation functions for improved signal detection and parameter estimation

A compilation of several correlation functions which were developed by the author and have been used for several years in signal analysis applications is given. The affine invariant pseudometric is a correlation function normalized to be independent of power, DC bias, and phase rotation. It was developed to track radar video sync pulses. It has recently been successfully used to track glottal pulses in voiced speech. The cross-power spectrum represents a significant improvement over standard power-spectral methods for recovering weak stationary tones in noise. The harmonic rejecting correlation function is a variant of the Wigner transform which resolves fundamentals from harmonic and subharmonic features produced by periodic waveforms. Each of these algorithms has been tested and used on a variety of data. Most importantly, for each of the methods described here, closed form solutions are derived, which enable easy implementations.<>