Minimum bias multiple taper spectral estimation

Abstract

Two families of orthonormal tapers are proposed for multi-taper spectral analysis: minimum bias tapers, and sinusoidal tapers $\{{\mathbf{v}}^{(\mathbf{k})}\}$, where $v_n^{(k)}=\sqrt{\frac{2}{N+1}}\sin \frac{\pi kn}{N+1}$, and $N$ is the number of points. The resulting sinusoidal multitaper spectral estimate is $\hat{S}(f)=\frac{1}{2K(N+1)}{\sum }_{j=1}^K|y(f+\frac{j}{2N+2})-y(f-\frac{j}{2N+2}){|}^2$, where $y(f)$ is the Fourier transform of the stationary time series, $S(f)$ is the spectral density, and $K$ is the number of tapers. For fixed $j$, the sinusoidal tapers converge to the minimum bias tapers like $1/N$. Since the sinusoidal tapers have analytic expressions, no numerical eigenvalue decomposition is necessary. Both the minimum bias and sinusoidal tapers have no additional parameter for the spectral bandwidth. The bandwidth of the $j$th taper is simply $\frac{1}{N}$ centered about the frequencies $\frac{\pm j}{2N+2}$. Thus the bandwidth of the multitaper spectral estimate can be adjusted locally by simply adding or deleting tapers. The band limited spectral concentration, ${\int }_{-w}^w|V(f){|}^{2}df$, of both the minimum bias and sinusoidal tapers is very close to the optimal concentration achieved by the Slepian tapers. In contrast, the Slepian tapers can have the local bias, ${\int }_{-1/2}^{1/2}{f}^2|V(f){|}^{2}df$, much larger than of the minimum bias tapers and the sinusoidal tapers.

References in corpus (3)

• Optimal Data-based Kernel Estimation of Evolutionary Spectra
• Spectral Estimation of Plasma Fluctuations I: Comparison of Methods
• Function Estimation Using Data Adaptive Kernel Estimation - How Much Smoothing?

Cited by in corpus (15)

• Spatiospectral concentration on a sphere
• Slepian functions and their use in signal estimation and spectral analysis
• Spatiospectral concentration in the Cartesian plane
• Adaptive Smoothing of the Log-Spectrum with Multiple Tapering
• Kernel estimation of the instantaneous frequency
• Partial Coherence Estimation via Spectral Matrix Shrinkage under Quadratic Loss
• Adaptive spectral proper orthogonal decomposition of tonal flows
• On estimating the structure factor of a point process, with applications to hyperuniformity
• Random Matrix Derived Shrinkage of Spectral Precision Matrices
• Spectral estimation for spatial point processes and random fields
• MSE estimates for multitaper spectral estimation and off-grid compressive sensing
• Adaptive Frequency Band Analysis for Functional Time Series
• M${}^2$NuFFT: A Computationally Efficient Suboptimal Power Spectrum Estimator for Fast Exploration of Nonuniformly Sampled Time Series
• Signal Processing and Piecewise Convex Estimation
• On the Underspread/Overspread Classification of Random Processes