Spectral density estimation

About: Spectral density estimation is a research topic. Over the lifetime, 5391 publications have been published within this topic receiving 123105 citations.

MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing

Abstract: 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 analysis, Proc. IEEE, 1982]: assuming bandwidth $W$ and $N$ time domain observations, the average of the square of the first $K=\lfloor 2NW\rfloor$ Slepian functions approaches, as $K$ grows, an ideal bandpass kernel for the interval $[ -W,W]$ . We provide an analytic proof of this fact and measure the corresponding rate of convergence in $L^{1}$ norm. This validates a heuristic approximation used to control the MSE of the multitaper estimator. The estimates have also consequences for the method of compressive acquisition of multi-band signals introduced by Davenport and Wakin, giving MSE approximation bounds for the dictionary formed by modulation of the critical number of prolates.

A direct algorithm for computing 2-D AR power spectrum estimates

Abstract: An algorithm for computing the parameters in a 2-D autoregressive spectral estimate without prior estimation of the correlation is described. The algorithm utilizes the multichannel form of the Burg algorithm and the relation between multichannel and 2-D AR modeling. The procedure permits computation of the spectral matrix for several channels of 2-D data; models with support in different quadrants are combined to form the spectral estimate. >

Effects of additive noise on signal reconstruction from Fourier transform phase

Abstract: The effects of additive noise in the given phase on signal reconstruction from the Fourier transform phase are experimentally studied. Specifically, the effects on the sequence reconstruction of different methods of sampling the degraded phase of the number of nonzero points in the sequence, and of the noise level, are examined. A sampling method that significantly reduces the error in the reconstructed sequence is obtained, and the error is found to increase as the number of nonzero points in the sequence increases and as the noise level increases. In addition, an averaging technique is developed which reduces the effects of noise when the continuous phase function is known. Finally, as an illustration of how the results in this paper may be applied in practice, Fourier transform signal coding is considered. Coding only the Fourier transform phase and reconstructing the signal from the coded phase is found to be considerably less efficient (i.e., a higher bit rate is required for the same mean-square error) than reconstructing from both the coded phase and magnitude.

Spectral Estimation of Plasma Fluctuations I: Comparison of Methods

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.

IVDST: A Fast Algorithm for Atomic Norm Minimization in Line Spectral Estimation

Abstract: This letter presents a fast algorithm named iterative Vandermonde decomposition and shrinkage-thresholding (IVDST), which offers a low-complexity solution to atomic norm minimization (ANM) in off-grid compressed sensing for line spectral estimation from few measurements. It implements the ANM principle via the accelerated proximal gradient (APG) technique, without invoking computationally expensive semidefinite programming (SDP). To approximate the proximal operator in each APG iteration, Vandermonde decomposition is applied to utilize the Toeplitz structure inherent in the line spectral model, and the low-rank property of the Toeplitz-structured matrix is enforced via a simple shrinkage-thresholding operation. The IVDST algorithm effectively reduces the order of computational complexity compared to SDP-based solutions. It also offers an explicit way to bridge the ANM principle with classic super-resolution line spectral estimation algorithms, such as MUSIC.