A multiple window method for estimation of peaked spectra

A multiple window method for estimation of the peaked power density spectrum is designed. The method optimizes a filter function utilizing the Karhunen-Loeve basis functions of a known peaked spectrum as windows to reduce variance and bias in the locality of the frequency peak. For improving performance, a penalty function is used to suppress the sidelobes outside a given bandwidth. The improved windows are obtained as the solution of a generalized eigenvalue problem. The bias at the frequency peak is reduced due to matching windows, while the variance is decreased by averaging uncorrelated periodograms. The method is compared with the Thomson multiple window estimator as well as to a single Hanning window in a simulation.

[1]  D. Thomson,et al.  Spectrum estimation and harmonic analysis , 1982, Proceedings of the IEEE.

[2]  Donald B. Percival,et al.  The variance of multitaper spectrum estimates for real Gaussian processes , 1994, IEEE Trans. Signal Process..

[3]  C. T. Mullis,et al.  Quadratic Estimators of the Power Spectrum , 1989 .

[4]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[5]  Joël Le Roux,et al.  A cost minimization approach for optimal window design in spectral analysis of sampled signals , 1992, IEEE Trans. Signal Process..

[6]  David J. Thomson,et al.  An overview of multiple-window and quadratic-inverse spectrum estimation methods , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.