Accurate Spectrum Estimation Research Articles

Fast and Accurate Spectrum Estimation via Virtual Coarray Interpolation Based on Truncated Nuclear Norm Regularization

Compared with the Nyquist sampling scheme, the coprime sampling scheme reduces the requirement of sampling rate significantly and simultaneously shows high degrees of freedom. Actually, the information received by the sampler is not fully utilized due to the non-uniformity of derived second-order virtual coarray. In addition, the virtual signals corresponding to the non-uniform virtual coarray may be contaminated by noise, which could affect the accuracy of spectrum estimation. In this letter, we propose a novel virtual coarray interpolation method for the inexact Toeplitz covariance matrix based on truncated nuclear norm regularization. The missing elements and exact covariance matrix can be obtained simultaneously by solving the covariance matrix completion problem that contains the error term and non-Toeplitz errors propagation control term. Simulation results demonstrate the superiorities of the proposed spectrum estimation method in terms of accuracy and computational complexity.

A registration-free approach for statistical process control of 3D scanned objects via FEM

Recent work in on-line Statistical Process Control (SPC) of manufactured 3-dimensional (3-D) objects has been proposed based on the estimation of the spectrum of the Laplace-Beltrami (LB) operator, a differential operator that encodes the geometrical features of a manifold and is widely used in Machine Learning (i.e., Manifold Learning). The resulting spectra are an intrinsic geometrical feature of each part, and thus can be compared between parts to assess the state of the manufacturing process while avoiding part to part registration (or “part localization”) pre-processing or the need for equal size meshes, characteristics which are required in previous approaches for SPC of 3D parts. The recent spectral SPC methods, however, are limited to monitoring surface data from objects such that the scanned meshes have no boundaries, holes or missing portions. In this paper we extend spectral methods by first considering a more accurate and general estimator of the LB spectrum that is obtained by application of Finite Element Methods (FEM) to the solution of Helmholtz's equation with boundaries. It is shown how the new spectral FEM approach, while it retains the advantages of not requiring part localization/registration or equal size datasets scanned from each part, it provides more accurate spectrum estimates, which results in faster detection of out of control conditions than earlier methods, can be applied to both mesh or volumetric (solid) scans, and furthermore, it is shown how it can be applied to partial scans that result in open meshes (surface or volumetric) with boundaries, increasing the practical applicability of the methods. The present work brings SPC methods closer to contemporary research in Computer Graphics and Manifold Learning. MATLAB code that reproduces the examples of this paper is provided in the supplementary materials.

Linear-Prediction-Based Accurate Spectrum Estimation with Pitch Extension for Bone-Conducted Speech

Linear-Prediction-Based Accurate Spectrum Estimation with Pitch Extension for Bone-Conducted Speech

Uncertainty analysis of the measured spectrum obtained using transmission grating spectrometer

Transmission grating spectrometer is applied in the area of inertial confinement fusion and other laser plasma interaction experiments. Accurate spectrum estimation depends on the measurement uncertainty. Based on the transmission grating diffraction efficiency calibration experiments, the uncertainty of diffraction efficiency is analyzed. Then the uncertainty of X-ray spectrum unfolding progress is investigated. The total uncertainty of the measured spectrum is obtained for 0.1 to 5 keV.

Fault Lengths During the Patras 1993 Earthquake Sequence as Estimated from the Pulse Width of Initial P Wave

Usually, earthquake source parameters are estimated using spectral techniques; the corner frequency is related to a source dimension through scaling laws that make assumptions about source geometry and rupture velocity, and the seismic moment is evaluated from the long-period spectral level (i.e., BRUNE, 1970). This conventional method however is not highly efficient when we deal with a large number of earthquakes, as in the present case. An alternative approach is based on the measured pulse width of the initial P wave at an observation station of far-field. Pulse width methods, like spectral methods, do not require precise measurement of pulse amplitudes or instrumental response. Unlike spectral methods, though, the pusle width methods only require a very short part of the first arriving signal, which is relatively free of other interfering waveforms such as reflection, scattering, or multiple travel paths (WU and LEES, 1996). In order to make accurate spectrum estimates, spectral methods typically use 0.5 to 2 sec of data, whereas the pulse width may be estimated over half a wavelength of the P-wave arrival. O’NEILL and HEALY (1973) proposed such an approach for a spherical source. FRANKEL (1981) applied this method for an expanding circular crack. FRANKEL and KANAMORI (1983) extended the initial P-wave pulse width method by