# Adaptive smoothing of the log-spectrum with multiple tapering

@article{Riedel1996AdaptiveSO, title={Adaptive smoothing of the log-spectrum with multiple tapering}, author={Kurt S. Riedel}, journal={IEEE Trans. Signal Process.}, year={1996}, volume={44}, pages={1794-1800} }

A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimated is performed, followed by kernel smoothing the log-multiple taper estimate. This procedure reduces the expected mean square error by (/spl pi//sup 2//4)/sup 4/5/ over simply smoothing the log tapered periodogram. A data-adaptive implementation of a variable-bandwidth kernel smoother is given.

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## References

SHOWING 1-10 OF 18 REFERENCES

### Optimal data-based kernel estimation of evolutionary spectra

- Computer ScienceIEEE Trans. Signal Process.
- 1993

Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain, where the optimal taper length is a small fraction of the optimal kernel halfwidth and the ratio of the ideal-frequency halfwidth to the optimal-time halfwidth is determined.

### Spectrum estimation and harmonic analysis

- MathematicsProceedings of the IEEE
- 1982

In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this…

### Multitaper estimation of the innovation variance of a stationary time series

- MathematicsIEEE Trans. Signal Process.
- 1995

It is demonstrated that the multiple tapering approach produces much better estimates of the innovations variance than the other methods when the spectrum has a high dynamic range and/or is rapidly varying.

### Spectral estimation of plasma fluctuations. I. Comparison of methods

- Environmental Science
- 1994

The relative root mean squared errors (RMSE) of nonparametric methods for spectral estimation is compared for microwave scattering data of plasma fluctuations. These methods reduce the variance of…

### Nonparametric Spectral Density Estimation Using Penalized Whittle Likelihood

- Mathematics
- 1994

Abstract The penalized likelihood approach is not well developed in time series analysis, even though it has been applied successfully in a number of nonparametric function estimation problems. Chow…

### Penalized Whittle Likelihood Estimation of Spectral Density Functions . 1

- Mathematics
- 1992

The penalized likelihood approach is not yet developed for time series problems, even though it has applied in a number of nonparametric function estimation problems. We define a new of nonparametric…

### Quadratic Estimators of the Power Spectrum

- Mathematics
- 1989

Abstract : Among nonparametric estimators of the power spectrum, quadratic estimators are the only ones that are dimensionally correct. This report motivates interest in quadratic estimators by…

### Minimum bias multiple taper spectral estimation

- PhysicsIEEE Trans. Signal Process.
- 1995

Two families of orthonormal tapers are proposed for multitaper spectral analysis: minimum bias tapers, and sinusoidal tapers {/spl upsisup (k/)}, where /spl upsisub nsup (k/)=/spl…