Reducing the bias of multitaper spectrum estimates

German A. Prieto, D. J. Thomson, Frank L. Vernon, & R. L. Parker

Published December 2007, SCEC Contribution #979

The power spectral density of geophysical signals provides information about the processes that generated them. We present a new approach to determine power spectra based on Thomson's multitaper analysis method. Our method reduces the bias due to the curvature of the spectrum close to the frequency of interest. Even while maintaining the same resolution bandwidth, bias is reduced in areas where the power spectrum is significantly quadratic. No additional sidelobe leakage is introduced. In addition, our methodology reliably estimates the derivatives (slope and curvature) of the spectrum. The extra information gleaned from the signal is useful for parameter estimation or to compare different signals.

Key Words
curvature, derivatives, inverse problem, multitaper spectrum

Prieto, G. A., Thomson, D., Vernon, F. L., & Parker, R. (2007). Reducing the bias of multitaper spectrum estimates. Geophysical Journal International, 171(3), 1269-1281. doi: 10.1111/j.1365-246X.2007.03592.x .