![]() (6)As it is seen in ( 6), in order for the bispectrum to be non-zero there should exist non-zero components, , and for some frequency sets. Therefore, the signal can be reconstructed from its bispectrum. In addition, the bispectrum can be used to reconstruct the amplitude of the FT of the signal . The exception is the linear phase (shifted signal), which will be lost by a bispectrum transform . The bispectrum can be used to extract the phase information which is lost in the power spectrum. the bispectrum of a signal is the same as the bispectrum of the shifted version of the same signal.Īnother property of the bispectrum transform is that it retains the phase information. ![]() Interestingly, a signal can be reconstructed uniquely from its bispectrum although the bispectrum is insensitive to shift in the domain in which the signal is recorded or sampled (e.g. More precisely, if the signal is zero mean and is independent of zero mean Gaussian noise, then the effect of noise will be eliminated. Therefore, if a signal is contaminated with Gaussian noise, the bispectrum of the signal removes or reduces the effect of such noise. One of these properties is that the bispectrum of a stationary signal with a Gaussian probability density function (PDF) with zero mean is zero. ![]() The bispectrum transform has some useful properties. The bispectrum has found applications in various fields including astronomy and cosmology , signal and image processing , interferometry applications , and mechanical , electrical , medical, and biomedical engineerings . For a stationary stochastic signal with zero mean, the moment and the cumulant are equal. The definition of bispectrum of a ‘stationary signal’ is given as both the FT of the moment or the cumulant . The bispectrum is defined as the Fourier transform (FT) of the third order cumulant or moment of a stationary signal and can be used as a noise reduction technique in some circumstances .
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