Recursive Computation of Trispectrum

Khalid Mahmood AAMIR  Mohammad Ali MAUD  Asim LOAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.10   pp.2914-2916
Publication Date: 2006/10/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.10.2914
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
power spectral density (PSD),  periodogram,  bispectrum,  trispectrum,  sliding DFT,  

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If the signal is not Gaussian, then the power spectral density (PSD) approach is insufficient to analyze signals and we resort to estimate the higher order spectra of the signal. However, estimation of the higher order spectra is even more time consuming, for example, the complexity of trispectrum is O(N 4). This problem becomes even more serious when short time Fourier transform (STFT) is computed - computation of the trispectrum is required after every shift of the window. In this paper, a method to recursively compute trispectrum has been presented and it is shown that the computational complexity, for a window size of N, is reduced to be O(N 3) and is the same as the space complexity.