A study of the effects in signal reconstruction from degraded Fourier transform phase

Summary form only given. The reconstruction of signals from phase only information has been treated. Although this is not possible in general, it has been shown previously that a finite duration sequence, provided its z-transform has no zeros in reciprocal pairs or on the unit circle, is uniquely specified by its Fourier transform phase within a scale factor and therefore can be reconstructed within a scale factor. The derivation assumes that the phases are known exactly; no error of any kind is involved. As all measured quantities are degraded by some kind of error, this assumption is much too restrictive when one wishes to reconstruct real signals as opposed to simulated signals. To study the effects of phase degradation on the quality of reconstructed signals, a series of experiments has been performed. The effects of additive random noise and of quantization noise in the phase samples have been investigated along with the effects of uniform and nonuniform sampling of the Fourier phase function. It has been found that the quality of a reconstructed signal is dependent on the choice of the set of frequencies used for sampling the Fourier phase function