DFT algorithm of the trispectrum reconstruction

As the bispectrum of the symmetric distribution random signals is equal to zero, whereas its trispectrum is not equal to zero, signal or system needs reconstructing from samples of the trispectrum of observation data. DFT algorithm for amplitude and phase reconstruction from trispectrum is proposed based on the bispectrum DFT algorithm. The magnitude and phase of the Fourier transform of a signal as well as those of the trispectrum are expanded into a series using a set of appropriate basis functions. Reconstruction is achieved by equating coefficients of like terms of these two expansions. Its advantage is that it only use the diagonal elements of amplitude and phase of the trispectrum, thus the computation is significantly reduced.