Title :
A Semiadaptive Smoothing Algorithm in Bispectrum Estimation
Author :
Yang, Wei ; Zurbenko, Igor G.
Author_Institution :
Center for Clinical Epidemiology & Biostat. (CCEB), Univ. of Pennsylvania, Philadelphia, PA
Abstract :
Fourier transform is used to calculate the third-order periodogram, which is an unbiased estimation of the bispectrum. However, the Fourier transform has energy leakage at adjacent frequencies, and the third-order periodogram is not a consistent estimator of the bispectrum because the variance does not converge toward zero when the sample size increases. To solve these problems, we used the Kolmogorov-Zurbenko Fourier transform (KZFT) to calculate the third-order periodogram and then adaptively smoothed it using a square window with varying bandwidth. At each paired frequencies, the bandwidth of the square window is expanded until the squared variation within the window reached a prespecified percentage of the total squared variation. The algorithm gave good results on simulated data, separating two close frequency components with very different energies in noisy data.
Keywords :
Fourier transforms; adaptive signal processing; parameter estimation; smoothing methods; spectral analysis; Kolmogorov-Zurbenko Fourier transform; adaptive smoothing; bispectrum estimation; energy leakage; semiadaptive smoothing algorithm; third-order periodogram; Adaptive Smoothing; Adaptive smoothing; Bispectrum; KZFT; Kologorov– Zurbenko Fourier transform (KZFT); Optimal Local Squared Variation; Third-Order Periodogram; bispectrum; optimal local squared variation; third-order periodogram;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2008.929131