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.

Spectral Analysis of a Univariate Process with Bad Data Points, via Maximum Entropy and Linear Predictive Techniques

Abstract: : A comparison of several methods for spectral estimation of a univariate process with equi-spaced samples, including maximum entropy, linear predictive, and autoregressive techniques, is made. The comparison is conducted via simulation for situations both with and without bad (or missing) data points. The case of bad data points required extensions of existing techniques in the literature and is documented fully here in the form of processing equations and FORTRAN programs. It is concluded that the maximum entropy (Burg) technique is as good as any of the methods considered, for the univariate case. The methods considered are particularly advantageous for short data segments. This report also reviews several available techniques for spectral analysis under different states of knowledge and presents the interrelationships of the various approaches in a consistent notation. Hopefully, this non-rigorous presentation will clarify this method of spectral analysis for readers who are nonexpert in the field.

High-Accuracy Spectrum Analysis of Sampled Discrete Frequency Signals by Analytical Leakage Compensation

Abstract: A method is presented which estimates the spectrum of a uniform sampled signal, which is sinusoidal, periodic, or composed of sinusoids of arbitrary frequencies. The proposed algorithm uses the Fast Fourier Transform algorithm. If frequency resolution is sufficient to distinguish different tones, the algorithm eliminates leakage and gives unbiased and highly accurate estimates for the amplitudes, phases, and frequencies.

A Unified Approach to Sparse Signal Processing

Abstract: A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described succinctly. The common benefits of significant reduction in sampling rate and processing manipulations are revealed. The key applications of sparse signal processing are sampling, coding, spectral estimation, array processing, component analysis, and multipath channel estimation. In terms of reconstruction algorithms, linkages are made with random sampling, compressed sensing and rate of innovation. The redundancy introduced by channel coding in finite/real Galois fields is then related to sampling with similar reconstruction algorithms. The methods of Prony, Pisarenko, and MUSIC are next discussed for sparse frequency domain representations. Specifically, the relations of the approach of Prony to an annihilating filter and Error Locator Polynomials in coding are emphasized; the Pisarenko and MUSIC methods are further improvements of the Prony method. Such spectral estimation methods is then related to multi-source location and DOA estimation in array processing. The notions of sparse array beamforming and sparse sensor networks are also introduced. Sparsity in unobservable source signals is also shown to facilitate source separation in SCA; the algorithms developed in this area are also widely used in compressed sensing. Finally, the multipath channel estimation problem is shown to have a sparse formulation; algorithms similar to sampling and coding are used to estimate OFDM channels.

Spectral estimation on a sphere in geophysics and cosmology

Abstract: We address the problem of estimating the spherical-harmonic power spectrum Sl of a statistically isotropic scalar signal s(r) from noise-contaminated data d(r) = s(r) + n(r) on a region R of the unit sphere. Three different methods of spectral estimation are considered: (i) the spherical analogue of the 1-D periodogram, (ii) the maximum likelihood method, and (iii) a spherical analogue of the 1-D multitaper method. The periodogram exhibits strong spectral leakage, especially for small regions of area A << 4π, and is generally unsuitable for spherical spectral analysis applications, just as it is in 1-D. The maximum likelihood method is particularly useful in the case of nearly whole-sphere coverage, A=4π, and has been widely used in cosmology to estimate the spectrum of the cosmic microwave background radiation from spacecraft observations. The spherical multitaper method affords easy control over the fundamental tradeoff between spectral resolution and variance, and is easily implemented, requiring neither non-linear iteration nor large-scale matrix inversion. As a result, the method is ideally suited for routine applications in geophysics, geodesy or planetary science, where the objective is to obtain a spatially localized estimate of the spectrum of a signal s(r) from data d(r) = s(r)+n(r) within a pre-selected and typically small region R.

Mammographic structure: data preparation and spatial statistics analysis

Abstract: Detection of tumors in mammograms is limited by the very marked statistical variability of normal structure rather than image noise. This presentation reports investigation of the statistical properties of patient tissue structures in digitized x-ray projection mammograms, using a database of 105 normal pairs of craniocaudal images. The goal is to understand statistical properties of patient structure, and their effects on lesion detection, rather than the statistics of the images per se, so it was necessary to remove effects of the x-ray imaging and film digitizing procedures. Work is based on the log-exposure scale. Several algorithms were developed to estimate the breast image region corresponding to a constant thickness between the mammographic compression plates. Several analysis methods suggest that the tissue within that region, assuming second- order stationarity, is described by a power law spectrum of the form P(f) equals A/f(beta ), where f is radial spatial frequency and (beta) is about 3. There is no evidence of a flattening of the spectrum at low frequencies. Power law processes can have a variety statistical properties that seem surprising to an intuition gained using mildly random processes such as smoothed Gaussian or Poisson noise. Some of these will be mentioned. Since P(f) is approximately a 3rd order pole at zero frequency, spectral estimation is challenging.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.