Linear Predictive Spectral Analysis via the Lp Norm

This study involves linear predictive spectral analysis under the general LP norm; both one dimensional and two dimensional spectral estimation algorithms are developed. The objective in this study is determination of frequency resolution capability for various LP normed solutions to linear predictive spectral estimation equations. A modified residual steepest descent algorithm is utilized to generate the required solution. The research presented in this thesis could not have been accomplished without the support of the Oklahoma State University Research Consortium For Well Log Data Enhancement Via Signal Processing. The member companies of this consortium include Amococ Production Company, Area Oil and Gas Company, Cities Service Oil and Gas Corporation, Conoco, Exxon, IBM, Mobil Research and Development, Phillips Petroleum Corporation, Sohio Petroleum Company, and Texaco.Electrical Engineerin

Application of Swept-Sine Excitation for Acoustic Impedance Education

The NASA Langley Normal Incidence Tube (NIT) and Grazing Flow Impedance Tube (GFIT) are regularly employed to characterize the frequency response of acoustic liners through the eduction of their specific acoustic impedance. Both test rigs typically use an acoustic source that produces sine wave signals at discrete frequencies (Stepped-Sine) to educe the impedance. The current work details a novel approach using frequency-swept sine waveforms normalized to a constant sound pressure level for excitation. Determination of the sound pressure level and phase from microphone measurements acquired using swept-sine excitation is performed using a modified Vold-Kalman order tracking filter. Four acoustic liners are evaluated in the NIT and GFIT with both stepped-sine and swept-sine sources. Using these two methods, the educed impedance spectra are shown to compare favorably. However, the new (Swept-Sine) approach provides much greater frequency resolution in less time, allowing the acoustic liner properties to be studied in much greater detail

An Overdetermined System for Improved Autocorrelation Based Spectral Moment Estimator Performance

Autocorrelation based spectral moment estimators are typically derived using the Fourier transform relationship between the power spectrum and the autocorrelation function along with using either an assumed form of the autocorrelation function, e.g., Gaussian, or a generic complex form and applying properties of the characteristic function. Passarelli has used a series expansion of the general complex autocorrelation function and has expressed the coefficients in terms of central moments of the power spectrum. A truncation of this series will produce a closed system of equations which can be solved for the central moments of interest. The autocorrelation function at various lags is estimated from samples of the random process under observation. These estimates themselves are random variables and exhibit a bias and variance that is a function of the number of samples used in the estimates and the operational signal-to-noise ratio. This contributes to a degradation in performance of the moment estimators. This dissertation investigates the use autocorrelation function estimates at higher order lags to reduce the bias and standard deviation in spectral moment estimates. In particular, Passarelli's series expansion is cast in terms of an overdetermined system to form a framework under which the application of additional autocorrelation function estimates at higher order lags can be defined and assessed. The solution of the overdetermined system is the least squares solution. Furthermore, an overdetermined system can be solved for any moment or moments of interest and is not tied to a particular form of the power spectrum or corresponding autocorrelation function. As an application of this approach, autocorrelation based variance estimators are defined by a truncation of Passarelli's series expansion and applied to simulated Doppler weather radar returns which are characterized by a Gaussian shaped power spectrum. The performance of the variance estimators determined from a closed system is shown to improve through the application of additional autocorrelation lags in an overdetermined system. This improvement is greater in the narrowband spectrum region where the information is spread over more lags of the autocorrelation function. The number of lags needed in the overdetermined system is a function of the spectral width, the number of terms in the series expansion, the number of samples used in estimating the autocorrelation function, and the signal-to-noise ratio. The overdetermined system provides a robustness to the chosen variance estimator by expanding the region of spectral widths and signal-to-noise ratios over which the estimator can perform as compared to the closed system

Coding Prony's method in MATLAB and applying it to biomedical signal filtering

Background:The response of many biomedical systems can be modelled using a linear combination of damped exponential functions. The approximation parameters, based on equally spaced samples, can be obtained using Prony's method and its variants (e.g. the matrix pencil method). This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB and analyses how they perform with synthetic and multifocal visual-evoked potential (mfVEP) signals. This paper briefly describes the theoretical basis of four polynomial Prony approximation methods: classic, least squares (LS), total least squares (TLS) and matrix pencil method (MPM). In each of these cases, implementation uses general MATLAB functions. The features of the various options are tested by approximating a set of synthetic mathematical functions and evaluating filtering performance in the Prony domain when applied to mfVEP signals to improve diagnosis of patients with multiple sclerosis (MS). Results:The code implemented does not achieve 100%-correct signal approximation and, of the methods tested, LS and MPM perform best. When filtering mfVEP records in the Prony domain, the value of the area under the receiver-operating-characteristic (ROC) curve is 0.7055 compared with 0.6538 obtained with the usual filtering method used for this type of signal (discrete Fourier transform low-pass filter with a cut-off frequency of 35 Hz). Conclusions:This paper reviews Prony's method in relation to signal filtering and approximation, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation. It emphasizes the importance of improving the computational methods used to implement the various methods described above.Universidad de AlcaláSecretaría de Estado de Investigación, Desarrollo e Innovació

Overspecified normal equations for spectral estimation

"June 1983." Originally published as thesis (Dept. of Electrical Engineering and Computer Science, M.S., 1983).Bibliography: p. 68-69.Supported in part by the Advanced Research Projects Agency monitored by ONR under Contract N00014-81-K-0742 NR-049-506 Supported in part by the National Science Foundation under Grant ECS80-07102by David Izraelevitz

Robust parametric modeling of speech in additive white Gaussian noise

ABSTRACT: In estimating the linear prediction coefficients for an autoregressive spectral model, the concept of using the Yule-Walker equations is often invoked. In case of additive white Gaussian noise (AWGN), a typical parameter compensation method involves using a minimal set of Yule-Walker equation evaluations and removing a noise variance estimate from the principal diagonal of the autocorrelation matrix. Due to a potential over-subtraction of the noise variance, however, this method may not retain the symmetric Toeplitz structure of the autocorrelation matrix and there- by may not guarantee a positive-definite matrix estimate. As a result, a significant decrease in es- timation performance may occur. To counteract this problem, a parametric modelling of speech contaminated by AWGN, assuming that the noise variance can be estimated, is herein presented. It is shown that by combining a suitable noise variance estimator with an efficient iterative scheme, a significant improvement in modelling performance can be achieved. The noise variance is esti- mated from the least squares analysis of an overdetermined set of p lower-order Yule-Walker eq- uations. Simulation results indicate that the proposed method provides better parameter estimates in comparison to the standard Least Mean Squares (LMS) technique which uses a minimal set of evaluations for determining the spectral parameters

Bias Removal Approach in System Identification and Arma Spectral Estimation

Electrical Engineerin

Bayesian Interpolation and Parameter Estimation in a Dynamic Sinusoidal Model

In this paper, we propose a method for restoring the missing or corrupted observations of nonstationary sinusoidal signals which are often encountered in music and speech applications. To model nonstationary signals, we use a time-varying sinusoidal model which is obtained by extending the static sinusoidal model into a dynamic sinusoidal model. In this model, the in-phase and quadrature components of the sinusoids are modeled as first-order Gauss–Markov processes. The inference scheme for the model parameters and missing observations is formulated in a Bayesian framework and is based on a Markov chain Monte Carlo method known as Gibbs sampler. We focus on the parameter estimation in the dynamic sinusoidal model since this constitutes the core of model-based interpolation. In the simulations, we first investigate the applicability of the model and then demonstrate the inference scheme by applying it to the restoration of lost audio packets on a packet-based network. The results show that the proposed method is a reasonable inference scheme for estimating unknown signal parameters and interpolating gaps consisting of missing/corrupted signal segments