Spectrum estimation by wavelet thresholding of multitaper estimators

Current methods for power spectrum estimation by wavelet thresholding use t he empirical wavelet coefficients derived from the log periodogram. Unfortu nately, the periodogram is a very poor estimate when the true spectrum has a high dynamic range and/or is rapidly varying. In addition, because the di stribution of the log periodogram is markedly non-Gaussian, special wavelet -dependent thresholding schemes are needed. These difficulties can be bypas sed by starting with a multitaper spectrum estimator. The logarithm of this estimator is close to Gaussian distributed if a moderate number (greater t han or equal to 5) of tapers are used. In contrast to the log periodogram, log multitaper estimates are not approximately pairwise uncorrelated at the Fourier frequencies, but the form of the correlation can be accurately and simply approximated. For scale-independent thresholding, the correlation a cts in accordance with the wavelet shrinkage paradigm to suppress small-sca le "noise spikes" while leaving informative coarse scale coefficients relat ively unattenuated. This simple approach to spectrum estimation is demonstr ated to work very well in practice. Additionally, the progression of the va riance of wavelet coefficients with scale can be accurately calculated, all owing the use of scale-dependent thresholds. This more involved approach al so works well in practice but is not uniformly preferable to the scale-inde pendent approach.