Least-squared error reconstruction of a deterministic sampled signal Fourier transform logarithm from its N-th order polyspectrum logarithm

Abstract This communication shows that a reconstruction formula proposed by Tekalp and Erdem yields the best least squared error estimate of the Fourier transform logarithm of a (deterministic) sampled signal when one of its higher order spectra logarithm is given. This property is deduced from the projection theorem and is mainly a consequence of the periodicity of the Fourier transform of sampled signals.