Spectral Estimation of Plasma Fluctuations I: Comparison of Methods

TL;DR

This paper compares various spectral estimation methods for plasma fluctuations, showing that hybrid methods combining multiple tapers and smoothing outperform traditional approaches in reducing error.

Contribution

It introduces and evaluates hybrid spectral estimation methods, including new adaptive multi-taper weightings, demonstrating superior performance over existing techniques.

Findings

Hybrid method with four tapers and kernel smoothing performs best.

Optimized smoothed tapered periodogram has 24% higher RMSE than hybrid method.

New adaptive multi-taper weightings outperform Thomson's original weighting.

Abstract

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 the periodogram estimate by averaging the spectrum over a frequency bandwidth. As the bandwidth increases, the variance decreases, but the bias error increases. The plasma spectra vary by over four orders of magnitude, and therefore, using a spectral window is necessary. We compare the smoothed tapered periodogram with the adaptive multiple taper methods and hybrid methods. We find that a hybrid method, which uses four orthogonal tapers and then applies a kernel smoother, performs best. For 300 point data segments, even an optimized smoothed tapered periodogram has a 24 \% larger relative RMSE than the hybrid method. We present two new adaptive multi-taper weightings which outperform Thomson's original adaptive weighting.