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.

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part II: Methods and results.

Abstract: Various alternative spectral estimation methods are examined and compared in order to assess their possible application for real-time analysis of Doppler ultrasound arterial signals. Specifically, five general frequency domain models are examined, including the periodogram, the general autoregressive moving average (ARMA) model which has the autoregressive (AR) and moving average (MA) models as special cases, and Capon's maximum likelihood spectral model. A simulated stationary Doppler signal with a known theoretical spectrum was used as the reference test sequence, and white noise was added to enable various signal/noise conditions to be created. The performance of each method representative of each spectral model was assessed using both qualitative and quantitative schemes that convey information related to the bias and variance of the spectral estimates. Three integrated performance indices were implemented for quantitative analysis. The relative computational complexity for each algorithm was also investigated. Our results indicate that both the AR(Yule-Walker) and ARMA(singular value decomposition) models of orders (8) and (4, 4), respectively, show good agreement with the theoretical spectrum, and yield estimates with variances considerably less than the Fast Fourier Transform (FFT). Preliminary results obtained with these methods using a clinical, non-stationary Doppler signal supports these observations.

Modeling of time delay and its application to estimation of nonstationary delays

Abstract: A method to model a time delay by a finite impulse response filter is presented. It is useful in simulation work that involves time delays and transforms the time delay estimation problem into one of parameter estimation. The benefits of this approach are the elimination of spectral estimation, a choice of many parameter estimation algorithms, and the capability to track time-varying delays. Two examples of estimating nonstationary time delays are also given.

Direct strain estimation in elastography using spectral cross-correlation.

Abstract: Spectral estimation of tissue strain has been performed previously by using the centroid shift of the power spectrum or by estimating the variation in the mean scatterer spacing in the spectral domain. The centroid shift method illustrates the robustness of the direct, incoherent strain estimator. In this paper, we present a strain estimator that uses spectral cross-correlation of the pre- and postcompression power spectrum. The centroid shift estimator estimates strain from the mean center frequency shift, while the spectral cross-correlation estimates the shift over the entire spectrum. Spectral cross-correlation is shown to be more sensitive to small shifts in the power spectrum and, thus, provides better estimation for smaller strains when compared to the spectral centroid shift. Spectral cross-correlation shares all the advantages gained using the spectral centroid shift, in addition to providing accurate and precise strain estimation for small strains. The variance and noise properties of the spectral strain estimators quantified by their respective strain filters are also presented.

On power estimation in maximum entropy spectral analysis

Abstract: A conceptually simple method for power estimation in maximum entropy spectral analysis, based on evaluation of complex residues of the spectral density estimator, is suggested. Numerical integration of the peaks of the power density function is thus avoided. The agreement in simple cases with conventional estimates is demonstrated, and the explicit performance is analyzed in detail in a series of examples. The close connection between the residue power estimate and the estimate proposed recently by Pisarenko is pointed out. The method is particularly suitable for spectral decomposition of low noise time series with several harmonic components, because it allows a direct listing of frequency and power estimates, provides an indication of the purity of the obtained harmonic components and enhances the resolution of the maximum entropy spectral density estimator. Computing facilities with modern program libraries are required for efficient use of the method.

Adaptive filtering primer with MATLAB

Abstract: INTRODUCTION Signal Processing An Example Outline of the Text DISCRETE-TIME SIGNAL PROCESSING Discrete Time Signals Transform-Domain Representation of Discrete-Time Signals The Z-Transform Discrete-Time Systems Problems Hints-Solutions-Suggestions RANDOM VARIABLES, SEQUENCES, AND STOCHASTIC PROCESSES Random Signals and Distributions Averages Stationary Processes Special Random Signals and Probability Density Functions Wiener-Khinchin Relations Filtering Random Processes Special Types of Random Processes Nonparametric Spectra Estimation Parametric Methods of power Spectral Estimation Problems Hints-Solutions-Suggestions WIENER FILTERS The Mean-Square Error The FIR Wiener Filter The Wiener Solution Wiener Filtering Examples Problems Hints-Solutions-Suggestions EIGENVALUES OF RX - PROPERTIES OF THE ERROR SURFACE The Eigenvalues of the Correlation Matrix Geometrical Properties of the Error Surface Problems Hints-Solutions-Suggestions NEWTON AND STEEPEST-DESCENT METHOD One-Dimensional Gradient Search Method Steepest-Descent Algorithm Problems Hints-Solutions-Suggestions THE LEAST MEAN-SQUARE (LMS) ALGORITHM Introduction Derivation of the LMS Algorithm Examples Using the LMS Algorithm Equation Performance Analysis of the LMS Algorithm Equation Learning Curve Complex Representation of LMS Algorithm Problems Hints-Solutions-Suggestions VARIATIONS OF LMS ALGORITHMS The Sign Algorithms Normalized LMS (NLMS) Algorithm Variable Step-Size LMS (VSLMS) Algorithm The Leaky LMS Algorithm Linearly Constrained LMS Algorithm Self-Correcting Adaptive Filtering (SCAF) Transform Domain Adaptive LMS Filtering Error Normalized LMS Algorithms Problems Hints-Solutions-Suggestions LEAST SQUARES AND RECURSIVE LEAST-SQUARES SIGNAL PROCESSING Introduction to Least Squares Least-Square Formulation Least-Squares Approach Orthogonality Principle Projection Operator Least-Squares Finite Impulse Response Filter Introduction to RLS Algorithm Problems Hints-Solutions-Suggestions ABBREVIATIONS BIBLIOGRAPHY APPENDIX A: MATRIX ANALYSIS INDEX