Showing papers on "Spectral density estimation published in 1987"
TL;DR: In this paper, the adaptive multitaper spectral estimation method was applied to a number of high-resolution digital seismic records and compared the results to those obtained using standard single-taper spectral estimates.
Abstract: Spectral estimation procedures which employ several prolate spheroidal sequences as tapers have been shown to yield better results than standard single-taper spectral analysis when used on a variety of engineering data. We apply the adaptive multitaper spectral estimation method of Thomson (1982) to a number of high-resolution digital seismic records and compare the results to those obtained using standard single-taper spectral estimates. Single-taper smoothed-spectrum estimates are plagued by a trade-off between the variance of the estimate and the bias caused by spectral leakage. Applying a taper to reduce bias discards data, increasing the variance of the estimate. Using a taper also unevenly samples the record. Throwing out data from the ends of the record can result in a spectral estimate which does not adequately represent the character of the spectrum of nonstationary processes like seismic waveforms. For example, a discrete Fourier transform of an untapered record (i.e., using a boxcar taper) produces a reasonable spectral estimate of the large-amplitude portion of the seismic source spectrum but cannot be trusted to provide a good estimate of the high-frequency roll-off. A discrete Fourier transform of the record multiplied by a more severe taper (like the Hann taper) which is resistant to spectral leakage leads to a reliable estimate of high-frequency spectral roll-off, but this estimate weights the analyzed data unequally. Therefore single-taper estimators which are less affected by leakage not only have increased variance but also can misrepresent the spectra of nonstationary data. The adaptive multitaper algorithm automatically adjusts between these extremes. We demonstrate its advantages using 16-bit seismic data recorded by instruments in the Anza Telemetered Seismic Network. We also present an analysis demonstrating the superiority of the multitaper algorithm in providing low-variance spectral estimates with good leakage resistance which do not overemphasize the central portion of the record.
402 citations
TL;DR: In this paper, the role of the truncation/apodization function used to obtain the phase correction is discussed, as well as the special problem of emission spectra for one-sided interferograms.
Abstract: In high precision Fourier transform spectrometry, proper handling of the phase correction is essential if the full potential wave number accuracy of the data is to be preserved. One-sided interferograms are shown to be especially sensitive to phase error, and this sensitivity is quantitatively related to the signal-to-noise ratio. The role of the truncation/apodization function used to obtain the phase correction is also discussed, as is the special problem of emission spectra.
94 citations
IBM1
TL;DR: Most of the reduction in the variance of the variance estimate can be achieved with modest amounts of overlapping, which may have practical implications because of the large number of batches required for the statistical test of lack of correlation.
Abstract: The conventional method of batch means and the overlapping batch means approach of Meketon and Schmeiser are related to spectral estimation via the time averaging of subsequence periodograms. It is shown that most of the reduction in the variance of the variance estimate can be achieved with modest amounts of overlapping. This may have practical implications because of the large number of batches required for the statistical test of lack of correlation. and the usual practice of rebatching the data after this test is passed.
81 citations
TL;DR: Autoregressive modeling has been found to give better results when analysing small sample volumes obtained from a pulsed velocimeter (narrow spectrum), even for short data lengths.
Abstract: The spectral analysis of Doppler blood flow velocity signals enjoys wide-spread interest owing to the exhaustive information on the signal which it yields. The discrete Fourier transform is the most extensively used method of analysis. However, the statistical stability of such analysis is poor; spectral smoothing, which improves the statistical stability, also results in greater width and poorer resolution of the spectrum. Autoregressive modelling has been found to give better results when analysing small sample volumes obtained from a pulsed velocimeter (narrow spectrum), even for short data lengths.
53 citations
TL;DR: Inverse Fourier transform has been used to derive the gradient-index profiles of inhomogeneous films having spectral requirements and results show a good agreement with the theory and evidences the reliability of the technology used to produce inhomogeneity media.
Abstract: Inverse Fourier transform has been used to derive the gradient-index profiles of inhomogeneous films having spectral requirements. Two examples are given, and the corresponding experimental designs are presented. Results show a good agreement with the theory and evidences the reliability of the technology used to produce inhomogeneous media.
35 citations
01 Jan 1987
TL;DR: ESPRITJ is discussed in the context of direction-of-arrival estimation, it can be applied to a wide variety of problems, including spectral estimation, and has several advantages over earlier techniques such as MUSIC including improved performance, rcduccd computational load.
Abstract: A new approach to the general problem of 5ignal parameter estimation is described. Though the technique (ESPRITJ is discussed in the context of direction-of-arrival estimation, it can be applied to a.wide variety of problems ~ncluding spectral estimation. ESPRIT exploits an underlying roiaironnl invariance among signal subspaces induced by an array of sensors with a rransiationai invuriunce structure (e.g., pairwise matched and co-d~mtional antenna element douhlcts) and has several advantages over earlier techniques such as MUSIC ucluding improved performance, rcduccd computational load. freedom from array characterizahonl callbration, and reduced sensitiwty to array perturbations. Results of computer simulations carried out to evaluate the new algorithm arc proented.
35 citations
TL;DR: Two new fast algorithms are presented that adaptively compute a least squares estimate of the power spectrum of a time series by modeling the input as an AR signal of order m and simultaneous minimization of the sum of the forward and backward prediction error energies.
Abstract: Power spectrum estimation is of great importance in various applications of signal processing, such as geophysics and communications. In this paper two new fast algorithms are presented that adaptively compute a least squares estimate of the power spectrum of a time series. This is achieved by modeling the input as an AR signal of order m and simultaneous minimization of the sum of the forward and backward prediction error energies. The first algorithm is of the 0 (m2) type, and the second of 0(m) requiring 9m multiplications and additions.
32 citations
TL;DR: An initial crude estimate of source location can be used to develop refined estimates using processing algorithms which significantly reduce processing requirements when compared to those required using a comparable array when the number of anticipated sources existing over the field of view (FOV) is large.
Abstract: The processing simplifications which result in using a multiple beam antenna (MBA) as a spatial sensor for performing spectral estimation are considered. Sources are presumed to be located over a two-dimensional field of view characterized by the two angular coordinates \theta and \phi . The MBA configuration consists of an aperture (usually either a reflector or lens) illuminated by a collection of feeds located in its focal plane (see Fig. 1), followed by a switch network for selecting the outputs of any desired feed port. Using the MBA as the spatial sensor for performing spectral estimation, as contrasted to the array antenna configuration, has a distinct advantage: for a given collection of source wavefronts incident on the aperture, a crude estimate of each source position is obtained simply by monitoring the power output of each feed port. This is to be contrasted to the array configuration, where the average output power of each element port is the same, so long as the wavefronts incident on the aperture emanate from uncorrelated sources. As shall be developed further, this initial crude estimate of source location can be used to develop refined estimates using processing algorithms which significantly reduce processing requirements when compared to those required using a comparable array when the number of anticipated sources existing over the field of view (FOV) is large. Finally, since the spectral estimate of the source location is essentially an "open-loop" estimate, involving a priori measured quantities such as the antenna port radiation patterns, we consider the effects of measurement errors on the estimate. The results are normalized so as to be generally applicable to both the array antenna configuration as well as for the MBA.
29 citations
26 citations
01 Apr 1987
TL;DR: A new algorithm useful for extrapolation and Fourier analysis of discrete signals that are given by a relative small number of samples that can be applied to higher-dimensional problems.
Abstract: This paper describes a new algorithm useful for extrapolation and Fourier analysis of discrete signals that are given by a relative small number of samples. The extrapolation is based on the assumption that the discrete Fourier spectrum shows dominant spectral lines. Involving only FFT, the iterative algorithm is not restricted to one-dimensional signals but can also be applied to higher-dimensional problems. Additional knowledge on the signal like band-limitedness or positivity can easily be taken into account.
TL;DR: This approach, as Cadzow's singular value decomposition (SVD) method, has provided significantly higher performance spectral estimates for a low-order ARMA model than those obtained via usual techniques which are based upon direct solution of the MYW equations and which use a high-order model without considering an additive noise.
Abstract: This paper presents an approach to time series analysis and ARMA spectral estimation from only the output data corrupted by noise. It is shown that the generalized (not well-known) modified Yule-Walker (MYW) equations hold when the residual is some correlated noise. To solve such equations, a new version of the generalized least squares (GLS) method is proposed, yielding AR parameter estimates with higher accuracy. This GLS method can also be used to enhance the estimation accuracy of AR parameters for short and noisy data in case of the MYW equation holding theoretically. Furthermore, a simple procedure for improving MA parameter estimates is studied. Our approach, as Cadzow's singular value decomposition (SVD) method, has provided significantly higher performance spectral estimates for a low-order ARMA model than those obtained via usual techniques which are based upon direct solution of the MYW equations and which use a high-order model without considering an additive noise.
TL;DR: In this paper, a new technique for two-dimensional (2D) spectral estimation of a stationary random field (SRF) is investigated, which is based on the extension of the Radon transform theory to stationary random fields.
Abstract: A new technique for two-dimensional (2-D) spectral estimation of a stationary random field (SRF) is investigated in this paper. This is based on the extension of the Radon transform theory to stationary random fields (SRF's), proposed by Jain and Ansari [19]. Using the Radon transform, the 2-D estimation problem is reduced to a set of one-dimensional (1-D) independent problems, which could then be solved using 1-D linear prediction (LP) or by any other high-resolution estimation procedure. This is unlike previous methods which obtain the 2-D power spectral density OPSD) estimate by using 1-D high-resolution techniques in the spirit of a separable estimator [2]. Examples are provided to illustrate the performance of the new technique. Various features of this approach are highlighted.
01 Jan 1987
TL;DR: This work presents a technique for high resolution time-frequency signal analysis based on a modified version of the Wigner-Ville Distribution which can improve both spectral resolution and tracking of instantaneous frequency.
Abstract: We present a technique for high resolution time-frequency signal analysis based on a modified version of the Wigner-Ville Distribution (WVD). This is achieved by recognizing that the WVD is the Fourier Transform of a bilinear complex kernel and replacing the Fourier Transform by a high resolution model based spectral estimator. Singular value decomposition methods are employed to produce spectral estimates which are more robust to noise and less sensitive to model order. The results show that the modified WVD can improve both spectral resolution and tracking of instantaneous frequency.
06 Apr 1987
TL;DR: It is pointed out that a correspondence between RN+1space and discrete signals with duration of N+1 points can be set up, and the signals that can't be reconstructed from its end point and FT magnitude correspond to a subset of RN-1 with measure zero.
Abstract: In this paper, the reconstruction of discrete signal with finite time duration from its end point and Fourier Transform (FT) magnitude is considered. Based on one result of [1] that a class of discrete signal can be reconstructed from its FT magnitude and one end sample point, with the help of Measure Theory, furtherly we point out that a correspondence between RN+1space and discrete signals with duration of N+1 points can be set up, and the signals that can't be reconstructed from its end point and FT magnitude correspond to a subset of RN+1with measure zero. In other words, discrete signal with finite time duration can almost be uniquely reconstructed from its end point and FT magnitude.
01 Apr 1987
TL;DR: A three step method for obtaining nearly maximum likelihood ARMA spectral estimates is presented, which is comparable to Yule-Walker methods, but the method gives asymptotically efficient estimates.
Abstract: A three step method for obtaining nearly maximum likelihood ARMA spectral estimates is presented. The computational complexity of the algorithm is comparable to Yule-Walker methods, but the method gives asymptotically efficient estimates. The implementation of the algorithm is discussed, and numerical examples are presented to illustrate its performance.
TL;DR: A new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes and it is shown that the proposed algorithm will also reduce the bias in the estimated parameters.
Abstract: A new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes. The proposed algorithm consists of three stages. In the first stage, an autoregressive model is fitted and the residue obtained is used as an estimate of the noise. In the second stage, an autoregressive recursive moving average model is fitted using the residual of the first stage. A modified residual is then filtered using a parameter δ and the model obtained from the second stage to generate an improved estimate of the noise. In the third stage, this improved estimate of the noise is used to obtain a better autoregressive moving average model. It is shown that the proposed algorithm will also reduce the bias in the estimated parameters. The simulation results given show that the proposed filter compares favorably to the algorithm introduced by Mayne and Clark and also Landau. This filter is then applied to the adaptive line enhancement, sinusoidal detection, and adaptive spectral estimation problems to illustrate its usefulness.
06 Apr 1987
TL;DR: This paper addresses the problem of signal reconstruction from Fourier transform phase and presents the results of studies on reconstruction from partial phase and discusses the application of these results in speech analysis and coding.
Abstract: This paper addresses the problem of signal reconstruction from Fourier transform phase. In particular, we examine two aspects of this problem. First, we discuss signal reconstruction from the phase spectrum of the short-time Fourier transform(STFT). Next, we examine the problem of signal recovery from partial phase information. We present the results of our studies on reconstruction from partial phase and discuss the application of these results in speech analysis and coding.
01 Apr 1987
TL;DR: A new technique for 2-D spectral estimation of a stationary random field (SRF) is investigated, based on the extension of the Radon transform theory to stationary random fields, proposed by Jain and Ansari.
Abstract: A new technique for 2-D spectral estimation of a stationary random field (SRF) is investigated in this paper. This is based on the extension of the Radon transform theory to stationary random fields, proposed by Jain and Ansari [19]. Using Radon transform the 2-D estimation problem is reduced to a set of 1-D independent problems, which could then be solved using 1-D Linear Prediction (LP) or any other high resolution estimation procedure. This is unlike previous methods which obtains the 2-D Power Spectral Density (PSD) estimate by using 1-D high resolution techniques in the spirit of a separable estimator [2]. An example is provided to illustrate the performance of the new technique. Various features of this approach are highlighted.
01 Apr 1987
TL;DR: It is reported how the designer in a variational approach for spectral estimation has to select a set of constraints and it is shown that the selected set of constraint becomes more relevant, as concerns with the resulting quality of the estimate, than the objective function minimized or maximized in the procedure.
Abstract: This work describes the use of constraints in variational procedures for spectral analysis. It is reported how the designer in a variational approach for spectral estimation has to select a set of constraints. At the same time it is shown that the selected set of constraints becomes more relevant, as concerns with the resulting quality of the estimate, than the objective function minimized or maximized in the procedure. Finally, some examples are presented which are the result of considering correlation and envelope constraints and minimizing the correlation extrapolation energy.
01 Apr 1987
TL;DR: This paper consists in doing maximum likelihood identification of structured correlation matrix using two different structures corresponding to Toeplitz matrices and to matrices with DFT representation related to time invariant series.
Abstract: In spectral estimation spectra are usually derived from an AR or MA model fitted to the data. An implicit step common to these methods is the estimation of the correlation matrix. In this paper our approach consists in doing maximum likelihood identification of structured correlation matrix. We have used two different structures corresponding to Toeplitz matrices and to matrices with DFT representation. Both structures are related to time invariant series. We have studied the performances of the spectral estimates obtained from our correlation matrix. In particular we show mean square error versus SNR plots for the frequency estimation of two noisy sinusoids.
DOI•
01 May 1987
TL;DR: In this paper, a frequency domain approach to forecasting is presented, which is suitable for time series which have frequency components that are harmonically related, and involves the use of a Fast Fourier Transform algorithm which calculates the frequency spectrum of a discrete set of data points whose array size is not restricted to the set 2m, where m is an integer.
Abstract: A frequency domain approach to forecasting is presented, which is suitable for time series which have frequency components that are harmonically related. It involves the use of a Fast Fourier Transform algorithm which calculates the frequency spectrum of a discrete set of data points whose array size is not restricted to the set 2m, where m is an integer. The high resolution of the spectra obtained for New Zealand electricity short and medium term data enables the true components present in the time domain waveforms to be accurately identified. A modified time domain waveform by Inverse transforming is then determined which (containing only the true harmonic components) can be extrapolated to yield a forecast.
01 Apr 1987
TL;DR: This work describes an approach based on Dynamic Progamming for the optimal segmentation of speech spectra into Selective Linear Predictive segments to minimise the discrepancy between real and model spectra and thereby to produce effective spectral estimates of the original signal.
Abstract: The evaluation of accurate speech spectral estimates is of importance in many areas such as formant extraction, speaker/speech recognition etc. This work describes an approach based on Dynamic Progamming for the optimal segmentation of speech spectra into Selective Linear Predictive (LP) segments to minimise the discrepancy between real and model spectra and thereby to produce effective spectral estimates of the original signal. A modification of this technique then leads to a novel method for the production of accurate estimates of speech formant positions. This segmentation scheme is implemented for both isolated speech spectra and complete utterances to produce values which are finally incorporated into cascade formant synthesisers. These results are found to offer significant advantages over those available using conventional LP methods.
TL;DR: In this article, the Fourier transform of light-beam-induced current profiles is expressed in a closed form and the influence of the experimental errors on the estimate of the diffusion length and of the recombination velocity is evaluated.
Abstract: The observation that the Fourier transform of light‐beam‐induced current profiles can be expressed in a closed form leads to a new method for their analysis. This method takes full advantage of the knowledge of the profile line shape and does not depend critically on the details of the current asymptotic behavior. The Fourier transform can be quickly calculated, making possible the use of standard minimization procedures on a personal computer. The influence of the experimental errors on the estimate of the diffusion length and of the recombination velocity is evaluated.
TL;DR: In this paper, a high-resolution spectral estimation method for 2-D isotropic random fields with covariance functions equal to weighted sums of cylindrical harmonics is presented, taking maximal advantage of the symmetries implied by both the isotropy and the special covariance structure of these fields.
TL;DR: The canonical variate method of rational system identification is investigated here for its performance in a high-resolution spectral analysis environment and is capable of yielding significantly improved resolution and SNR performance for multiple sinusoids in noise as compared to the computationally efficient high-performance method of Cadzow.
Abstract: The canonical variate method of rational system identification is investigated here for its performance in a high-resolution spectral analysis environment. A computationally simple version of the method, due to White [9], is briefly reviewed and applied to several standard examples. It is found that, at the cost of some computational complexity, the method is capable of yielding significantly improved resolution and SNR performance for multiple sinusoids in noise as compared to the computationally efficient high-performance method of Cadzow [8], which can also yield a negative power spectral density estimate under certain conditions. Another interesting feature of this method is that it directly applies to the problem of spectral matrix estimation of a multidimensional time series.
Dissertation•
01 Jan 1987
01 Jan 1987
TL;DR: Two high resolution techniques for spectral estimation of random processes are described, based on the Maximum Entropy Method, and an application to radar system is shown in detail.
Abstract: Two high resolution techniques for spectral estimation of random processes are described. The estimate is obtained from samples of the autocorrelation function or directly from samples of the process. These techniques are based on the Maximum Entropy Method (MEM). After a review of the main points of this method, an application to radar system is shown in detail. First, the estimation of clutter spectrum is considered; then, this estimate is exploited to shape a filter for clutter cancellation and target echo enhancement. The processing algorithm is an adaptive one, and its performances are evaluated, by means of computer simulation, in term of Improvement Factor and speed of adaptation.
01 Apr 1987
TL;DR: Experimental results revealed its superiority over WD for multi-component signals, and an alternative to WD with improved performance for such signals was proposed, based on a consideration why WD offers high resolution.
Abstract: Wigner distribution (WD) can provide for high frequency- or time- resolution, but its nonlinear property poses problems when applied to signals with multiple frequency components. This paper proposes an alternative to WD with improved performance for such signals, based on a consideration why WD offers high resolution. The observed data is first converted to analytic signals, which are then subjected to Fourier transform after squaring. Experimental results revealed its superiority over WD for multi-component signals.