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.

On nonparametric spectral estimation

Abstract: In this paper the Cramer-Rao bound (CRB) for a general nonparametric spectral estimation problem is derived under a local smoothness condition (more exactly, the spectrum is assumed to be well approximated by a piecewise constant function). Furthermore it is shown that under the aforementioned condition the Thomson (TM) and Danieli (DM) methods for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator. Finally the statistical efficiency of the TM and DM as nonparametric PSD estimators is examined and also compared to the CRB for ARMA-based PSD estimation. In particular for broadband signals, the TM and DM almost achieve the derived nonparametric performance bound and can therefore be considered to be nearly optimal.

A Phase-Angle Estimation Method for Synchronization of Grid-Connected Power-Electronic Converters

Abstract: This paper proposes a positive-sequence phase-angle estimation method based on discrete Fourier transform for the synchronization of three-phase power-electronic converters under distorted and variable-frequency conditions. The proposed method is designed based on a fixed sampling rate and, thus, it can simply be employed for control applications. First, analytical analysis is presented to determine the errors associated with the phasor estimation using standard discrete Fourier transform in a variable-frequency environment. Then, a robust phase-angle estimation technique is proposed, which is based on a combination of estimated positive and negative sequences, tracked frequency, and two proposed compensation coefficients. The proposed method has one cycle transient response and is immune to harmonics, noises, voltage imbalances, and grid frequency variations. An effective approximation technique is proposed to simplify the computation of the compensation coefficients. The effectiveness of the proposed method is verified through a comprehensive set of simulations in Matlab software. Simulation results show the robust and accurate performance of the proposed method in various abnormal operating conditions.

The zoom FFT using complex modulation

Abstract: A recent paper by Yip discussed the zoom transform as derived from the defining equation of the FFT. This paper simplifies the concepts and removes some of the restrictions assumed by Yip; ie., the total number of points need not be a power of 2. The technique is based on first specifying the desired center frequency, bandwidth, and frequency resolution. The signal is then sampled, modulated, and lowpass filtered. This result is purposely aliased, then transformed using an FFT algorithm. The result is an M-point frequency spectra of the desired bandwidth centered about the center frequency with a higher degree of resolution than could be directly obtained using an M-point transform.

The MUSIC algorithm for sparse objects: a compressed sensing analysis

Abstract: The multiple signal classification (MUSIC) algorithm, and its extension for imaging sparse extended objects, with noisy data is analyzed by compressed sensing (CS) techniques. A thresholding rule is developed to augment the standard MUSIC algorithm. The notion of restricted isometry property (RIP) and an upper bound on the restricted isometry constant (RIC) are employed to establish sufficient conditions for the exact localization by MUSIC with or without noise. In the noiseless case, the sufficient condition gives an upper bound on the numbers of random sampling and incident directions necessary for exact localization. In the noisy case, the sufficient condition assumes additionally an upper bound for the noise-to-object ratio in terms of the RIC and the dynamic range of objects. This bound points to the super-resolution capability of the MUSIC algorithm. Rigorous comparison of performance between MUSIC and the CS minimization principle, basis pursuit denoising (BPDN), is given. In general, the MUSIC algorithm guarantees to recover, with high probability, s scatterers with random sampling and incident directions and sufficiently high frequency. For the favorable imaging geometry where the scatterers are distributed on a transverse plane MUSIC guarantees to recover, with high probability, s scatterers with a median frequency and random sampling/incident directions. Moreover, for the problems of spectral estimation and source localizations both BPDN and MUSIC guarantee, with high probability, to identify exactly the frequencies of random signals with the number of sampling times. However, in the absence of abundant realizations of signals, BPDN is the preferred method for spectral estimation. Indeed, BPDN can identify the frequencies approximately with just one realization of signals with the recovery error at worst linearly proportional to the noise level. Numerical results confirm that BPDN outperforms MUSIC in the well-resolved case while the opposite is true for the under-resolved case, giving abundant evidence for the super-resolution capability of the MUSIC algorithm. Another advantage of MUSIC over BPDN is the former's flexibility with grid spacing and the guarantee of approximate localization of sufficiently separated objects in an arbitrarily refined grid. The localization error is bounded from above by for general configurations and by for objects distributed in a transverse plane, in line with physical intuition.