Average Walsh Power Spectrum for Periodic Signals

A circular shift-invariant Walsh power spectrum for deterministic periodic sequences is defined. For a sequence with period N, the power spectrum is the average of the Walsh power spectra of all N possible distinct circular shifts. The Average Walsh Power Spectrum (AWPS) consists of (N/2) + 1 coefficients, each representing a distinct sequency. A fast transformation from the arithmetic autocorrelation function of a periodic sequence to its AWPS is presented.