Showing papers on "Spectral density estimation published in 1988"

Bayesian Spectrum Analysis and Parameter Estimation

Abstract: 1 Introduction.- 2 Single Stationary Sinusoid Plus Noise.- 3 The General Model Equation Plus Noise.- 4 Estimating the Parameters.- 5 Model Selection.- 6 Spectral Estimation.- 7 Applications.- 8 Summary and Conclusions.- A Choosing a Prior Probability.- B Improper Priors as Limits.- C Removing Nuisance Parameters.- D Uninformative Prior Probabilities.- E Computing the "Student t-Distribution".

A digital method of modeling quadratically nonlinear systems with a general random input

Abstract: Without assuming particular statistics of the input, a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time-invariant system that can be described by Volterra series of up to second order is presented. The method is tested and validated by analyzing input-output data of a known quadratically nonlinear system. It is used when there is little knowledge about the input statistics or the input is non-Gaussian. It is also noted that the ordinary coherence functions cannot be used in explaining the input-output power transfer relationship of a quadratic system excited by a non-Gaussian input signal. With respect to the practical application of the method, the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed. >

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.

Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences

Abstract: A nonparametric spectral estimation method is presented for bandlimited random processes that have been sampled at arbitrary points in one or more dimensions. The method makes simultaneous use of several weight sequences that depend on the set of sampling point, the signal band, and the frequency band being analyzed. These sequences are solutions to a generalized matrix eigenvalue problem and are termed generalized prolate spheroidal sequences, being extensions of the familiar discrete prolate spheroidal sequences. Statistics of the estimator are derived, and the tradeoff among bias, variance, and resolution is quantified. The method avoids several problems typically associated with irregularly sampled data and multidimensional processes. A related method is suggested that has nearly as good performance while requiring significantly fewer computations. >

A comparative study and assessment of Doppler ultrasound spectral estimation techniques. Part I: Estimation methods.

Abstract: When compared to the classical Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) approach, modern estimation methods offer the potential for achieving significant improvements in estimating the power density spectrum of Doppler ultrasound signals. Such improvements, for example, might enable minor flow disturbances to be detected, thereby improving the sensitivity in arterial disease assessment. Specifically, reduction in the variance and bias can be achieved, and this may enable disturbed flow to be detected in a more sensitive manner. The approach taken here, is to consider spectral estimation methods as a problem of fitting an assumed model to the Doppler signal. The models described assume that the signal is stationary. Since the Doppler signal is generally nonstationary, it is assumed that a short enough time window interval can be chosen over which the signal can be considered stationary. We shall review the various methods and when appropriate, relate them to the nature of the Doppler signal.

Frequency estimation by principal component AR spectral estimation method without eigendecomposition

Abstract: An eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix, which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse. It is shown using a computer simulation that compared to the forward-backward method, the proposed method enhances the threshold in SNR by about 6-8 dB. Further improvement is obtained by a simple subset selection method and a second eigenvalue filtering iteration. >

Effects of Noise, Time-Domain Damping, Zero-Filling and the FFT Algorithm on the “Exact” Interpolation of Fast Fourier Transform Spectra:

Abstract: A frequency-domain Lorentzian spectrum can be derived from the Fourier transform of a time-domain exponentially damped sinusoid of infinite duration. Remarkably, it has been shown that even when such a noiseless time-domain signal is truncated to zero amplitude after a finite observation period, one can determine the correct frequency of its corresponding magnitude-mode spectral peak maximum by fitting as few as three spectral data points to a magnitude-mode Lorentzian spectrum. In this paper, we show how the accuracy of such a procedure depends upon the ratio of time-domain acquisition period to exponential damping time constant, number of time-domain data points, computer word length, and number of time-domain zero-fillings. In particular, we show that extended zero-filling (e.g., a "zoom" transform) actually reduces the accuracy with which the spectral peak position can be determined. We also examine the effects of frequency-domain random noise and round-off errors in the fast Fourier transformation (FFT) of time-domain data of limited discrete data word length (e.g., 20 bit/word at single and double precision). Our main conclusions are: (1) even in the presence of noise, a three-point fit of a magnitude-mode spectrum to a magnitude-mode Lorentzian line shape can offer an accurate estimate of peak position in Fourier transform spectroscopy; (2) the results can be more accurate (by a factor of up to 10) when the FFT processor operates with floating-point (preferably double-precision) rather than fixed-point arithmetic; and (3) FFT roundoff errors can be made negligible by use of sufficiently large (> 16 K) data sets.

Directional Spectrum Estimation from a Bayesian Approach

Abstract: A new directional spectral estimation method using a Bayesian approach is proposed. The proposed method is examined for numerical simulation data, and the validity of the method is discussed. Some examples of the directional spectra estimated from field observation data attained at an offshore oil rig utilizing seven wave probes are also shown in this report. The major conclusions of the report are : (1) The proposed method can be applied for more than four arbitrarily mixed instrument array measurements. (2) It has a higher resolution power than other existing methods for estimating directional spectrum. (3) It is a better method for estimating directional spectra from the cross-power spectra contaminated with estimation errors. (4.) It is more adaptable to reformulation of the estimation equations as the study of structures of directional spectrum progesses.

Wigner Distribution Function: Relation to Short-Term Spectral Estimation, Smoothing, and Performance in Noise.

Abstract: : The properties and behavior of the Wigner Distribution Function (WDF) are investigated both analytically and by means of a number of simple informative examples. The lack of local temporal averaging when obtaining the instantaneous correlation function, and the lack of weighting the longer delay values when transforming to the instantaneous spectrum, are shown to be the causes of the deleterious interference effects that are inherent to the WDF. The equivalence of short-term spectral estimation to the smoothed WDF offers an attractive alternative with guaranteed positive distribution values and no interference effects. The performance of a processor which estimates the WDF of a signal waveform in the presence of additive noise is investigated in terms of the output mean, bias, and variance. Dependence on filtering the input and time-weighting is allowed and included in the analysis. Numerical application to a particular example is carried out. Keywords: Wigner distribution function; Short term spectral estimation; Smoothing; Noise performance; Linear frequency; Modulation; Interference effects; Gaussian amplitude modulation; Marginals; Moments; Spread of distribution; Positive distributions; Ambiguity function.

Application of prewhitening to AR spectral estimation of EEG

Abstract: Conventional fast Fourier transform (FFT) and autoregressive (AR) spectral estimation techniques do not always perform well when applied to short segments of single trial EEG. On this class of EEG signal, the conventional FFT-based methods can suffer from significant leakage problems while conventional AR methods can suffer from problems related to model order selection and retention of spectral information in the residuals. An established alternative to the conventional AR estimation scheme called prewhitened AR spectral estimation, which theoretically addresses these drawbacks, was applied to EEG signals. Relative comparisons of the performance of a conventional FFT-based estimate, the conventional AR estimate, and the prewhitened AR estimate on three different examples of real, short-segment, single-trial EEGs are presented. These comparisons demonstrate that the prewhitened AR method overcomes the inherent drawbacks of the conventional methods. >

Apparatus for, and method of, analyzing signals

Abstract: The spectral components of both an original signal and a shifted version of the signal, for example a signal which is subjected to a time delay relative to the original signal, are obtained by means of Fourier Transform. This gives sets of first and second spectral components corresponding respectively to the original signal and the shifted signal. The phases of at least one pair of corresponding first and second spectral components are obtained, and subtracted to give a phase difference. The first aspect of the method measures the frequency of corresponding constituent of the original signal from the said phase difference based on a prior knowledge of the amount of shift. Further, having measured the frequency, one can measure the initial phase and amplitude of corresponding constituent of the signal. A second aspect of the method and an apparatus measure the amount of shift between two received signals from the said phase difference by means of a prior knowledge of the frequency of corresponding constituent of the signal. A third aspect of the method and an apparatus detect the existence of dominant constituent of the signal. This approach compares the difference in phases between adjacent spectral components of a signal with a constant value, (1-1/N)π. The measured signals can vary temporally or spatially.

Signal analysis and estimation : an introduction

Abstract: Discrete transforms, random signals and spectral estimation are stressed in this advanced-level text on Fourier analysis. Treatment is applicable to optical, acoustic and electrical signals. The text is divided into two main sections: deterministic signals and random signals. Initial chapters cover the analysis of continuous and discrete deterministic signals, and later chapters treat the properties, spectral analysis and estimation of random signals. Examples aim to assist the reader in understanding complex concepts and are often related to engineering applications - radar, antennae, tomography, analog and digital filters - illustrating how the techniques being studied are applied in practice.

Time-frequency and time-scale (signal processing)

Abstract: General results are presented for time-frequency and time-scale methods. Attention is given to both linear (short-time Fourier transform, wavelet transform) and bilinear (Wigner-Ville distribution, affine Wigner distribution) approaches, with emphasis put on their relationships. Also considered is the relationship of the methods examined to such approaches as constant-Q analysis and ambiguity functions. >

High-resolution Velocity Spectra Using Eigenstructure Methods

Abstract: Stacking spectra provide maximum‐likelihood estimates for the stacking velocity, or for the ray parameter, of well separated reflections in additive white noise. However, the resolution of stacking spectra is limited by the aperture of the array and the frequency of the data. Despite these limitations, parametric spectral estimation methods achieve better resolution than does stacking. To improve resolution, the parametric methods introduce a parsimonious model for the spectrum of the data. In particular, when the data are modeled as the superposition of wavefronts, the properties of the eigenstructure of the data covariance matrix can be used to obtain high‐resolution spectra. The traditional stacking spectra can also be expressed as a function of the data covariance matrix and directly compared to the eigenstructure spectra. The superiority of the latter in separating closely interfering reflections is then apparent from a simple geometric interpretation. Eigenstructure methods were originally developed...

Application of fast Fourier transform to auditory evoked brainstem response.

Abstract: The current application of fast Fourier transform (FFT) to the analysis of auditory evoked brainstem response (ABR) is reviewed under four categories: (1) digital filtering, which facilitates isolation of fast and slow components from the same ABR wave, is the most common use of FFT; (2) power spectral analysis: this seems significant in ABR for isolating and analysing slow, middle and fast components from the Fourier components around each peak of the power spectrum with a three-peak pattern by inverse fast Fourier transform; (3) cross correlation function shows the relationship between two signals being analysed from the viewpoint of their phase. Clinical applications are used in the diagnosis of multiple sclerosis and for automatic detection of ABR; and (4) phase spectral analysis: the synchrony measure method (Fridman, 1984) is a type of phase spectral analysis. In this method, the phase variances of selected Fourier components are calculated, from among 10 averaging groups of 200 sweeps in the same stimulating conditions, to determine the presence or absence of a response. The clinical application of this method to the automatic evaluation of ABR is discussed.

Method of carrier frequency estimation

Abstract: A method is provided for searching a wide, high-noise frequency band for a narrow, phase-modulated signal to determine the approximate carrier frequency of a data signal. The method comprises the steps of sampling a received signal at a rate sufficiently high to cover the search bandwidth, performing an efficient Fourier transform on the sampled signal to obtain a discrete point power spectral density, filtering each frequency component of the power spectral density with averaging filters, analyzing the filtered components to find the area of greatest power concentration, and computing the center frequency of the area of greatest power concentration. The method determines the approximate carrier frequency of a data signal quickly and efficiently for use in starting or detecting loss of lock in a frequency-locked demodulator.

Signal synthesis from modified discrete short-time transform

Abstract: The discrete short-time transform (DSTT) is a generalization of the discrete short-time Fourier transform (DSTFT). The necessary and sufficient conditions on the analysis filter, under which perfect reconstruction of the input signal is possible (when the DSTT is not modified), are presented. The class of linear modifications for which the original input can be reconstructed when the modification is applied is characterized. The synthesis of an optimal (in the minimum-mean-square-error sense) signal from a modified DSTT (MDSTT) of finite duration is presented. It is shown that for an analysis filter length that does not exceed a given value, the optimal synthesis scheme is independent of the duration of the given MDSTT and is an extension of the weighted overlap add (WOLA) synthesis method. For longer analysis filters, the optimal synthesis scheme becomes quite cumbersome, and therefore, a steady-state solution (as the duration of the MDSTT approaches infinity) is presented for this case. It is shown that this solution can be approximated with arbitrarily small reconstruction error. >

An efficient Fourier transform algorithm for frequency domains of several decades using logarithmically spaced time samples

Abstract: Discrete Fourier transforms are derived which allow the use of nonequally spaced time-domain samples. It is shown that the use of equal spacings in the logarithmic time and frequency domains provides a very efficient transform algorithm. The applicability of this algorithm for the analysis of systems with moderate dynamic behavior over several frequency decades is demonstrated by examples. An error analysis is given. >

Compensation of nonstationary harmonics using active power filter with Prony's spectral estimation

Abstract: A novel control scheme for the filter is proposed that is based on the cosine timing control principle and is easily realized with the microcomputer software. The output current waveform of the filter can be determined in real time. Prony's spectral estimation is introduced for measuring the nonstationary harmonic currents. The time-varying harmonic spectrum obtained by Prony's method shows more reasonable results than Fourier analysis. The compensating ability of the filter is verified through numerical analysis studies. >

Comparison between myoelectric signal mean and median frequency estimates

Abstract: This work was undertaken to compare the mean and median frequency properties and to evaluate the agreement between theoretical expectations and experimental findings. The relationship between mean and median frequency estimates and spectral estimation algorithms was also investigated. The results indicate that the mean frequency estimate is affected by a standard deviation about 25% lower than that of the median frequency, regardless of the estimation algorithm used. However, in clinical instrumentation the median frequency remains the preferred parameter, because of the relatively simpler computational procedure needed to estimate it online and its lower sensitivity to noise. >

Formant estimation algorithm based on pole focusing offering improved noise tolerance and feature resolution

Abstract: The ability to measure the centre frequencies of areas of resonance (formants) in the short-time power spectrum of speech is of paramount importance in the recognition of voiced speech sounds in a feature-extraction-based continuous speech recognition system. Additionally, the provision of a tracking algorithm, by which the loci of formants with respect to time can be estimated, yields formant transition information which helps identify phonetic features which are of short duration. Noise robustness in formant estimation is an essential attribute for recognition systems which are used in the office environment and in military applications. The novel technique presented in the paper provides a noise-robust method of extracting formant centre-frequency information from the short-time speech spectrum, and consequently improves the signal/noise performance of the associated formant tracking algorithm. Formant estimation is based on modelling the vocal tract frequency response using linear prediction coding (LPC) techniques. However, the estimation of formant centre frequency in any given analysis frame is greatly improved by employing off-axis spectral estimation coupled with a progressive increase in vocal tract model order, which together provide vocal tract pole enhancement. Finally, the use of a formant weighting filter function applied within each frame aids in conferring high noise immunity to the estimation process. The pole focusing technique is shown to offer an improvement of at least 14 dB in signal/noise immunity as a formant frequency estimator over conventional LPC-based spectral estimation. In its application to formant tracking, it is shown that the technique also offers improved separation of formants which tend to merge, besides offering a general improvement in the provision of formant detail, in particular with regard to weak nasal formants. An additional advantage of the technique is its relative insensitivity to choice of vocal tract model order, w

Minimum variance spectral estimation for broadband source location using steered covariance matrices

Abstract: An approach is presented for reducing the threshold observation time required to perform high resolution broadband bearing estimation. The proposed technique is based on a space-time statistic called the steered covariance matrix (STCM). In broadband settings, the STCM has an advantage over the well-known cross-spectral density matrix (CSDM) in that it can be estimated with much greater statistical stability. The STCM is used in conjunction with minimum variance spectral estimation to obtain a broadband spatial spectral estimate with a much lower threshold observation time than the CSDM-based minimum-variance distortionless response (MVDR) method. >

An efficient maximum entropy technique for 2-D isotropic random fields

Abstract: A linear MEM (maximum-entropy spectral estimation method) algorithm for 2-D isotropic random fields is introduced. Unlike general 2-D covariances, isotropic covariance functions that are positive definite on a disk are known to be extendible. A computationally efficient procedure is developed for computing the MEM isotropic covariance function that is given over a finite disk of radius 2R. It is shown that the isotropic MEM problem has a linear solution and that it is equivalent to the problem of constructing the optimal linear filter for estimating the underlying isotropic field at a point on the boundary of a disk radius R, given noisy measurements of the field inside the disk. The procedure is guaranteed to yield a valid isotropic spectral estimate and is computationally efficient since it requires only O(BRL/sup 2/) operations, where L is the number of points used to discretize the interval (0, R) and B is the bandwidth in the wave-number plane of the spectrum that to be estimated. Examples are presented to illustrate the behaviour of the algorithm and its high-resolution property. >

Automated two speaker separation system

Abstract: An algorithm designed to improve results for separating two voices simultaneously recorded on a single channel is presented. A variable frame size orthogonal transform and a spectral matching technique are used. A multistep pitch detection scheme is proposed which includes a traditional autocorrelation function, a modified autocorrelation, the average magnitude difference function, and a look-forward and look-backward double checking scheme. The orthogonal transforms utilized include the fast Fourier transform and the fast triangular transform. For a variable frame size transform, a prime factor fast Fourier transform has been developed. The execution of the process is automated and implemented on the IBM-PC, VAX 8650, and HP 9000. Intelligibility tests using simple quantitative measures have been performed on the separated signals. An extension of the problem to the three-speaker case is reported. >

The performance of Fourier transform division multiplexing schemes on peak limited channels

Abstract: Inherent in the method of Fourier transform division multiplexing (FTDM) is the possibility that the FTDM encoder will yield spurious power bursts, which can affect the linearity of the channel. A common way for dealing with such bursts is to clip the signal at some predetermined peak power level. The authors obtain explicit formulas for the probability distributions of such bursts and for the errors that the clipping induce in the decoder. The formulas can help the FTDM code designer to decide on an appropriate average power constraint. >

Robust Spectral Estimation: Autocorrelation Based Minimum Free Energy Method

Abstract: A new spectral estimation theory is developed which has its conceptual roots in the theory of statistical thermodynamics The new parametric estimation theory is called minimum free energy (MFE) estimation Here, in analogy with thermodynamics, a free energy objective function is defined as a linear combination of an error energy and a signal entropy expression The MFE estimated signal model parameters are commensurate with the global minimum of the free energy function Statistical analyses of simulations at low SNR's show that MFE is a robust low variance spectral estimator capable of generating high resolution spectral replication from sin- gle snapshot data The relative merits of MFE are substantiated by simulations comparing MFE with the Tufts-Kurnaresari signal sub- space, noise reduced, modified covariance algorithm