摘要:

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.

DOI:10.1049/ip-f-1.1983.0033

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0034

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0035

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0036

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0037

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0038

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0039

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0040

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0041

出版商:IEE    

年代:1983

数据来源: IET

摘要:

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.

DOI:10.1049/ip-f-1.1983.0042

出版商:IEE    

年代:1983

数据来源: IET