Recursive Computation of Wiener-Khintchine Theorem and Bispectrum

Khalid Mahmood AAMIR  Mohammad Ali MAUD  Arif ZAMAN  Asim LOAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.1   pp.321-323
Publication Date: 2006/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.1.321
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Digital Signal Processing
power spectral density (PSD),  Wiener-Khintchine theorem,  periodogram,  bispectrum,  

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Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach in case the signal is Gaussian. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. This paper presents a recursive form of PSD to reduce the complexity. If the signal is not Gaussian, the PSD approach is insufficient and we estimate the higher order spectra of the signal. Estimation of higher order spectra is even more time consuming. In this paper, recursive versions for computation of bispectrum has been presented as well. The computational complexity of PSD and bispectrum for a window size of N, are O(N) and O(N2) respectively.