On the zeros of the linear prediction-error filter for deterministic signals
01 Feb 1983-IEEE Transactions on Acoustics, Speech, and Signal Processing (IEEE)-Vol. 31, Iss: 1, pp 217-220
TL;DR: In this article, the exponent parameters of a linear prediction-error filter polynomial for a class of deterministic signals, that are a sum of samples of M exponentially damped/undamped sinusoids, are studied.
Abstract: The zeros of a linear prediction-error filter polynomial for a class of deterministic signals, that are a sum of samples of M exponentially damped/undamped sinusoids, is studied. It is assumed that N samples are available for processing and that they are uncorrupted by noise. It is shown that the exponent parameters of the M signals can be determined from M zeros (called "signal zeros") of an Lth degree prediction-error filter polynomial (L>M) if L lies in between M and N - M (N - M/2 in a special case). The rest of the L - M zeros of the filter polynomial switch are called extraneous zeros, are shown to be approximately uniformly distributed with in the unit circle, regardless of the type of exponentials in the signal, if the prediction filter coefficients are chosen to have minimum Euclidean length. The results obtained provide insight into the estimation problem with noisy data.
Citations
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TL;DR: In this paper, the estimation procedure presented here makes use of "backward prediction" in addition to singular value decomposition (SVD) for accurate estimation of closely spaced frequencies of sinusoidal signals in noise.
Abstract: We have presented techniques [1] - [6] based on linear prediction (LP) and singular value decomposition (SVD) for accurate estimation of closely spaced frequencies of sinusoidal signals in noise. In this note we extend these techniques to estimate the parameters of exponentially damped sinusoidal signals in noise. The estimation procedure presented here makes use of "backward prediction" in addition to SVD. First, the method is applied to data consisting of one and two exponentially damped sinusoids. The choice of one and two signal components facilitates the comparison of estimation error in pole damping factors and pole frequencies to the appropriate Cramer-Rao (CR) bounds and to traditional methods of linear prediction. Second, our method is applied to an example due to Steiglitz [8] in which the data consists of noisy values of the impulse response samples (composed of many exponentially damped sinusoids) of a linear system having both poles and zeros. The poles of the system are accurately determined by our method and the zeros are obtained subsequently, using Shanks' method.
881 citations
TL;DR: Prony analysis as mentioned in this paper extends Fourier analysis by directly estimating the frequency, damping, strength, and relative phase of modal components present in a given signal, which can be used to extract such information from transient stability program simulations and from large-scale system tests of disturbances.
Abstract: Prony analysis extends Fourier analysis by directly estimating the frequency, damping, strength, and relative phase of modal components present in a given signal. The ability to extract such information from transient stability program simulations and from large-scale system tests of disturbances would be quite valuable to power system engineers. Early results of the application of this method to stability program output are reported. Also included are benchmarks against known models and a brief mathematical summary. >
873 citations
TL;DR: In this article, a polynomial D(z) with special properties is constructed from the eigenvectors of C, the zeros of which give estimates of the angle of arrival.
Abstract: The problem of estimating the angles of arrival of M plane waves incident simultaneously on a line array with L + 1 (L?M) sensors utilizing the special eigenstructure of the covariance matrix C of the signal plus noise at the output of the array is addressed. A polynomial D(z) with special properties is constructed from the eigenvectors of C, the zeros of which give estimates of the angle of arrival. Although the procedure turns out to be essentially the same as that developed by Reddi, the development presented here provides insight into the estimation problem.
867 citations
TL;DR: In this article, the authors extensively review operational modal analysis approaches and related system identification methods and compare them in an extensive Monte Carlo simulation study, and then compare the results with the results obtained in an experimental setting.
Abstract: Operational modal analysis deals with the estimation of modal parameters from vibration data obtained in operational rather than laboratory conditions. This paper extensively reviews operational modal analysis approaches and related system identification methods. First, the mathematical models employed in identification are related to the equations of motion, and their modal structure is revealed. Then, strategies that are common to the vast majority of identification algorithms are discussed before detailing some powerful algorithms. The extraction and validation of modal parameter estimates and their uncertainties from the identified system models is discussed as well. Finally, different modal analysis approaches and algorithms are compared in an extensive Monte Carlo simulation study.
481 citations
01 Jan 1993
TL;DR: A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques.
Abstract: A unified approach is presented to the related problems of recovering signal parameters from noisy observations and identifying linear system model parameters from observed input/output signals, both using singular value decomposition (SVD) techniques. Both known and new SVD-based identification methods are classified in a subspace-oriented scheme. The SVD of a matrix constructed from the observed signal data provides the key step in a robust discrimination between desired signals and disturbing signals in terms of signal and noise subspaces. The methods that are presented are distinguished by the way in which the subspaces are determined and how the signal or system model parameters are extracted from these subspaces. Typical examples, such as the direction-of-arrival problem and system identification from input/output measurements, are elaborated upon, and some extensions to time-varying systems are given. >
344 citations
References
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Book•
01 Jun 1974
TL;DR: Since the lm function provides a lot of features it is rather complicated so it is going to instead use the function lsfit as a model, which computes only the coefficient estimates and the residuals.
Abstract: Since the lm function provides a lot of features it is rather complicated. So we are going to instead use the function lsfit as a model. It computes only the coefficient estimates and the residuals. Now would be a good time to read the help file for lsfit. Note that lsfit supports the fitting of multiple least squares models and weighted least squares. Our function will not, hence we can omit the arguments wt, weights and yname. Also, changing tolerances is a little advanced so we will trust the default values and omit the argument tolerance as well.
6,956 citations
01 Apr 1975
TL;DR: This paper gives an exposition of linear prediction in the analysis of discrete signals as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal.
Abstract: This paper gives an exposition of linear prediction in the analysis of discrete signals The signal is modeled as a linear combination of its past values and present and past values of a hypothetical input to a system whose output is the given signal In the frequency domain, this is equivalent to modeling the signal spectrum by a pole-zero spectrum The major part of the paper is devoted to all-pole models The model parameters are obtained by a least squares analysis in the time domain Two methods result, depending on whether the signal is assumed to be stationary or nonstationary The same results are then derived in the frequency domain The resulting spectral matching formulation allows for the modeling of selected portions of a spectrum, for arbitrary spectral shaping in the frequency domain, and for the modeling of continuous as well as discrete spectra This also leads to a discussion of the advantages and disadvantages of the least squares error criterion A spectral interpretation is given to the normalized minimum prediction error Applications of the normalized error are given, including the determination of an "optimal" number of poles The use of linear prediction in data compression is reviewed For purposes of transmission, particular attention is given to the quantization and encoding of the reflection (or partial correlation) coefficients Finally, a brief introduction to pole-zero modeling is given
4,206 citations
01 Nov 1981
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
Abstract: A summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented in this tutorial. An examination of the underlying time series model assumed by each technique serves as the common basis for understanding the differences among the various spectrum analysis approaches. Techniques discussed include the classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods. A summary table in the text provides a concise overview for all methods, including key references and appropriate equations for computation of each spectral estimate.
2,941 citations
TL;DR: In this paper, a new method for retrieving harmonics from a covariance function is introduced, based on a theorem of Caratheodory about the trigonometrical moment problem.
Abstract: Summary
A new method for retrieving harmonics from a covariance function is introduced. The method is based on a theorem of Caratheodory about the trigonometrical moment problem. The relation between this method and the ‘maximum entropy’ spectral estimator is discussed, and the effect of a small addition of a noise component is investigated. A numerical example is discussed.
1,148 citations