相关论文: Thomson's Multitaper Method Revisited

At the heart of non-parametric spectral estimation, lies the dilemma known as the bias-variance trade-off: low biased estimators tend to have high variance and low variance estimators tend to have high bias. In 1982, Thomson introduced a…

The use of multitaper estimates for spectral proper orthogonal decomposition (SPOD) is explored. Multitaper and multitaper-Welch estimators that use discrete prolate spheroidal sequences (DPSS) as orthogonal data windows are compared to the…

An adaptive algorithm for spectral proper orthogonal decomposition (SPOD) of mixed broadband-tonal turbulent flows is developed. Sharp peak resolution at tonal frequencies is achieved by locally minimizing the bias of the spectrum. Smooth…

Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…

We obtain estimates for the Mean Squared Error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic…

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…

Multitaper estimators have enjoyed significant success in estimating spectral densities from finite samples using as tapers Slepian functions defined on the acquisition domain. Unfortunately, the numerical calculation of these Slepian…

We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied…

Two families of orthonormal tapers are proposed for multi-taper spectral analysis: minimum bias tapers, and sinusoidal tapers $\{ \bf{v}^{(k)}\}$, where $v_n^{(k)}=\sqrt{\frac{2}{N+1}}\sin\frac{\pi kn}{N+1}$, and $N$ is the number of…

abridged] A method to rapidly estimate the Fourier power spectrum of a point distribution is presented. This method relies on a Taylor expansion of the trigonometric functions. It yields the Fourier modes from a number of FFTs, which is…

Background: Windowed Fourier decompositions (WFD) are widely used in measuring stationary and non-stationary spectral phenomena and in describing pairwise relationships among multiple signals. Although a variety of WFDs see frequent…

While the Lomb-Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60-year history of developing…

We characterize the practical receiver in a wide range of signal intensity for optical wireless communication, from discrete pulse regime to continuous waveform regime. We first propose a statistical non-linear model based on the…

Nonuniformly sampled signals are prevalent in real-world applications. However, estimating their power spectra from finite samples poses a significant challenge. The optimal solution-Bronez Generalized Prolate Spheroidal Sequence (GPSS) by…

In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle…

We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…

A test based on tapering is proposed for use in testing a global linear hypothesis under a functional linear model. The test statistic is constructed as a weighted sum of squared linear combinations of Fourier coefficients, a tapered…

We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…

For nonparametric inference about a function, multiscale testing procedures resolve the need for bandwidth selection and achieve asymptotically optimal detection performance against a broad range of alternatives. However, critical values…