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Communications, Radar and Signal Processing, IEE Proceedings F

Issue 3 • Date April 1983

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Displaying Results 1 - 16 of 16
  • Spectral analysis

    Page(s): 193 - 194
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    Freely Available from IEEE
  • Efficient algorithm for ARMA spectral estimation

    Page(s): 195 - 201
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    An ARMA spectral estimation technique based on the modified Yule-Walker equations is presented. Several recursive lattice algorithms are proposed for estimating the AR and MA spectral parameters. These computationally efficient algorithms provide spectral estimates of different orders. The choice of the AR model order and its effect on the quality of the spectral estimates are briefly discussed. View full abstract»

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  • Singular-value decomposition approach to time series modelling

    Page(s): 202 - 210
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    In various signal processing applications, as exemplified by spectral analysis, deconvolution and adaptive filtering, the parameters of a linear recursive model are to be selected so that the model is `most¿¿ representative of a given set of time series observations. For many of these applications, the parameters are known to satisfy a theoretical recursive relationship involving the time series' autocorrelation lags. Conceptually, one may then use this recursive relationship, with appropriate autocorrelation lag estimates substituted, to effect estimates for the operator's parameters. A procedure for carrying out this parameter estimation is given which makes use of the singular-value decomposition (SVD) of an extended-order autocorrelation matrix associated with the given time series. Unlike other SVD modelling methods, however, the approach developed does not require a full-order SVD determination. Only a small subset of the matrix's singular values and associated characteristic vectors need be computed. This feature can significantly alleviate an otherwise overwhelming computational burden that is necessitated when generating a full-order SVD. Furthermore, the modelling performance of this new method has been found empirically to excel that of a near maximum-likelihood SVD method as well as several other more traditional modelling methods. View full abstract»

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  • Statistical efficiency of correlation-based methods for ARMA spectral estimation

    Page(s): 211 - 217
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    The paper considers bounds on the statistical efficiency of the estimators of the poles and zeros of an ARMA process based on estimates of the process autocorrelation function. Special attention is paid to autoregressive and autoregressive plus white noise processes. A measure of the statistical variability of the estimates is introduced as the ratio of the Cramer-Rao bounds on the generalised variances of estimates based on the unreduced data and on the autocorrelation function. Numerical values of this measure are presented for several processes of interest. Estimator performance is then related to pole-zero locations and the signal/noise ratio. View full abstract»

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  • Experimental comparison of three multichannel linear prediction spectral estimators

    Page(s): 218 - 229
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    Single-channel spectral estimators based on linear prediction techniques, such as the maximum-entropy method, have been shown to often provide better spectral stability and resolution than standard FFT procedures for short data sequences. Based on this improved performance, a multitude of multichannel linear prediction techniques have been promoted for processing multichannel data sequences. Three of these are examined in the paper: a multichannel generalisation of the single-channel Burg algorithm by Nuttall, a maximum-entropy type of algorithm by Morf, Vieira, Lee and Kailath, and a multichannel extension of the covariance method of linear prediction implemented by Marple. For purposes of experimental comparison, various two-channel data sets were processed by the three methods to produce the two autospectra, the magnitude-squared coherence and the coherence phase associated with each data set. A possible deleterious effect of signal `feed-across¿¿ between autospectra and in the coherence has been discovered in all three methods. The phenomenon, due to inexact pole-zero cancellation, is especially prominent for short data sequences. Based on the multichannel results given here, the Nuttall method generally produced the best spectral estimates. View full abstract»

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  • Duality for multidimensional MEM spectral analysis

    Page(s): 230 - 235
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    The solution to the general multidimensional MEM spectral estimation problem is described. A detailed derivation of the dual optimisation problem, in which entropy is minimised, is given. A necessary and sufficient condition for the existence of a solution to the general problem is presented. The theory is also extended to a `correlation-approximating¿¿ MEM spectral estimate. Algorithms applicable to the dual problem are discussed. View full abstract»

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  • Unifying approach to spectral estimation

    Page(s): 236 - 238
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    The paper presents a unified conceptual derivation of some spectral estimation methods, including the maximum-entropy method and the classical window method. Two reasonable requirements provide the starting point, leading to various mathematical formulations. A data-dependent window method is derived from one of them, and an objective criterion for the selection of the free parameters of the window is outlined. View full abstract»

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  • Analysis of a generalised framework for spectral estimation. Part 1: The technique and its mean value

    Page(s): 239 - 241
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    The paper presents a generalised framework for spectral estimation. Included in the framework are the classical Blackman-Tukey and widely used weighted overlapped segment averaging methods. An analysis and discussion of the mean value of the spectral estimate is provided here. Part 2 of the paper presents results on the variance of the technique. View full abstract»

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  • Analysis of a generalised framework for spectral estimation. Part 2: Reshaping and variance results

    Page(s): 242 - 245
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    The capabilities of lag reshaping for the generalised spectral estimation technique, in order to realise desirable effective windows, is illustrated for several combinations of temporal and lag weightings. Also the variance of the spectral estimate is presented and computed for some windows with very good sidelobe behaviour. It is found that, with proper overlap, if the length of the temporal weighting is somewhat larger than the length of the lag weighting, the variance is at a near minimum relative to any technique which realises the same frequency resolution with the given finite data record length. View full abstract»

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  • Spectral estimation using an adaptive oscillator

    Page(s): 246 - 249
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    The paper presents experimental results and comments relating to an adaptive oscillator structure proposed recently by Griffiths. A possible lattice structure for the new adaptive filter is also given. View full abstract»

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  • New algorithm for spectrum estimation and an associated VLSI design

    Page(s): 250 - 255
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    By treating the reflection coefficients as independent variables, a new recursive algorithm is introduced which results in a lower prediction error and stable filters. Its performance is evaluated using sine waves in noise and pulse Doppler radar data, and is found to be substantially better than those of Burg's algorithm, Makhoul's covariance-lattice method and Marple's least-squares algorithm. Thus, although a lower error is not always desirable, the above procedure leads to better spectra for the type of data used. The spectrum of the new algorithm is the same as that of Fougere's algorithm whenever the latter reaches a solution, but its speed is substantially higher and it avoids `oscillations¿¿, which made the previous computational requirements excessive. The higher speed is mainly achieved by using the covariance instead of the data in the iterations, and the `oscillations¿¿ are avoided by introducing a relaxation procedure. A regular structure of VLSI implementation is also introduced. View full abstract»

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  • Remarks on the statistical behaviour of orthogonal beamforming

    Page(s): 256 - 260
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    Orthogonal beamforming is the name given to certain high-resolution methods for estimating the spectra of a wave field received by an array of sensors. These methods use the eigenvalues and eigenvectors of the spectral matrix of the sensor outputs. The problem is to predict the behaviour of such methods when only an estimate of the matrix is known. The sensor outputs may consist of sensor noise, ambient noise and noise from a finite set of discrete sources. The properties of the eigensystem of the spectral matrix in the case of weak ambient noise motivate the methods of orthogonal beamforming, for example Pisarenko's nonlinear peak estimates and the projection estimates of Owsley and Liggett. If the spectral matrix is estimated by one of the classical methods, some asymptotic distributional properties of the matrix estimate and its eigensystem are well known. They can be used to determine asymptotic expressions, for example for the first and second moments of the peak estimators, and to approximate the distributions. The parameters, however, cannot be calculated in applications since the eigensystem of the exact spectral matrix is required. Therefore we recently developed bounds for the deviation of the peak estimates which only use limited knowledge about the matrix. We applied some results on perturbations of Hermitian operators. The asymptotic behaviour of the bounds for the projection estimator is investigated, and possibilities for their estimation are indicated. Finally, we report on extensive simulations with random matrices to evaluate the new bounds. As a result, we found that the projection estimator behaves stably and that there are tight bounds if the eigenvalues of interest are sufficiently separated from the rest. View full abstract»

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  • Power estimation for an array of sensors and its use in broadband detection

    Page(s): 261 - 266
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    A power estimation technique is presented which is suitable for broadband detection of signals reaching a passive array of sensors. It is demonstrated that the technique provides a fixed beam pattern for all steering directions at low frequencies and that this may be used by an operator to aid detection. The effectiveness of the technique is demonstrated by comparison with two alternative approaches. View full abstract»

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  • Characteristic frequency responses of broadband adaptive arrays

    Page(s): 267 - 271
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    The interference direction frequency response and cancellation capability of a broadband tapped delay line adaptive array are discussed. The frequency response is found to be an entire function in the s-plane, but the hypothesis is advanced that, for a given total time delay and number of degrees of freedom, it approximates to the rational frequency response function of a single uniformly tapped delay line for band- limited interference spectra. Some elementary expressions for the cancellation are derived. View full abstract»

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  • Time delay estimation with receivers of approximately known phase difference characteristics

    Page(s): 272 - 278
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    The problem of measuring the time delay (or difference in arrival times) of a signal emanating from a source and received at two separate locations is considered. Most existing techniques of time delay estimation assume identical receivers. The phase of the cross-spectrum between the receivers' outputs is then directly proportional to frequency, with the time delay as the proportionality constant. The paper develops a new estimator for receivers having unequal phase characteristics. Their phase differences are represented by a polynomial in frequency, with the coefficients of the polynomial approximately known. An augmented least-squares estimator, incorporating the approximate phase information, is developed to compute the time delay. Simulation results that serve to illustrate the method and confirm some of the theoretical findings are presented. View full abstract»

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  • Spatial lattice filter for high-resolution spectral analysis of array data

    Page(s): 279 - 287
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    In the analysis of time/frequency domain signals, lattice filters have proved popular, providing significant advantages over conventional tapped delay line digital filters. Improvements in adaptation times and model order identification have been observed, and the modular structure of these filters allows a straightforward VLSI hardware implementation. In the paper, a lattice-structured spatial filter for use in adaptive arrays is described. This filter is shown to take on a triangular structure in the spatial domain which provides a step-by-step solution to the prediction problem. Several uses of the lattice filter in array processing are then discussed, particularly the extraction of high-resolution spatial spectral estimates from the parameters of the filter. These spatial spectral estimators include the maximum-entropy, maximum-likelihood and eigenvector (Pisarenko) based methods and are used to obtain high-resolution maps of the directional power incident upon an array of spatially distributed sensors. It is also shown how multiple look direction constraints may be applied to the lattice filter, providing the capability for enhancing desired signals in the presence of directional interference. View full abstract»

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Aims & Scope

The latest version of this title is Radar, Sonar & Navigation, IET.

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