Abstract
The bispectrum is the Fourier transform of the triple correlation, sometimes also referred to as triple product integral. We are concerned here with the bispectrum of the autotriple correlation. Bispectrum analysis can be used to solve phase problems in signal processing, since the knowledge of the bispectrum of a signal usually allows one to reconstruct both amplitude and phase of the Fourier transform signal. We present mathematical proof based on the theory of analytic functions and discuss the restrictions involved. A recursive algorithm is outlined for the reconstruction from sampled data. In addition, possibilities for noise reduction by averaging redundant information will be described. Examples are included for 1-D signals.
© 1984 Optical Society of America
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