Cadzow, J.A., 1982, "Spectral estimation: an overdetermined rational model equation approach,"Proceedings of the IEEE, Vol. 70, pp. 907-939.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the final prediction error (FPE) criterion [1] and the criterion for autoregressive transfer function (CAT) 16] can be regarded as application oriented. However, they work only for autoregressive (AR) models. Although numerous approaches have been proposed to obtain linear ARMA spectral estimates [6, 5, 7, 15], few authors have been involved in order selection. Cadzow[5, 6] proposed selection of the order by examining the normalized ratio u u( k of the extended order autocorrelation matrix estimate using a singular value decomposition. In this method, the order of the AR part is set equal to the ....

....transfer function (CAT) 16] can be regarded as application oriented. However, they work only for autoregressive (AR) models. Although numerous approaches have been proposed to obtain linear ARMA spectral estimates [6, 5, 7, 15] few authors have been involved in order selection. Cadzow[5, 6] proposed selection of the order by examining the normalized ratio u u( k of the extended order autocorrelation matrix estimate using a singular value decomposition. In this method, the order of the AR part is set equal to the smallest k for which u u( k is deemed adequately close to one. ....

Cadzow, J.A., 1982, "Spectral estimation: an overdetermined rational model equation approach,"Proceedings of the IEEE, Vol. 70, pp. 907-939.

....cost is modest but performance suffers even for moderate signal to noise ratios (SNRs) In contrast, parametric algorithms [5, 6] give good results but are computationally expensive. For time series analysis, several authors have used eigenvalue or singular value analysis in the detection problem [7, 8]. The basic idea there is to identify the dominant singular values (SVs) or eigenvalues) by some criterion (for instance, a pre chosen threshold) The number of the dominant SVs is the model order. The technique in [7] requires the selection of a pre determined threshold; both [7] and [8] suffer ....

....have used eigenvalue or singular value analysis in the detection problem [7, 8] The basic idea there is to identify the dominant singular values (SVs) or eigenvalues) by some criterion (for instance, a pre chosen threshold) The number of the dominant SVs is the model order. The technique in [7] requires the selection of a pre determined threshold; both [7] and [8] suffer from poor detection performance. With the help of perturbation analysis, Fuchs [9] developed a statistical criterion based on the data autocorrelation matrix to detect the number of sinusoids. The approach requires a ....

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J. A. Cadzow, "Spectral estimation: A overdetermined rational model equation approach," in Proc. IEEE, vol. 70, pp. 907--939, September 1982.

.... In signal processing, speech processing and system identification applications, one can often model signals as a stationary random sequence that is generated by passing white noise through a filter or system with a stable transfer function and letting the system come to a statistical steady state [5, 7, 16, 24, 25]. However, the generating filter or system is not known a priori in many real life situations. The system then has to be estimated from given observations, after which one can use the filter and the corresponding spectral density e.g. in design processes. In practice, only a finite number of ....

.... Nth order polynomials satisfies the interpolation condition at 1: 1 2 N (z) N (z) 1 2 c 1 z Gamma1 c 2 z Gamma2 : c N z GammaN : and is an all pole realization: w(z) p r N z N N (z) However, in many applications finite spectral zeros are desired [5, 7]. Based on the Szego polynomials, all solutions (up to order N ) of the interpolation problem (1) are described in the Kimura Georgiou parameterization [8, 14] v(z) 1 2 N (z) ff 1 N Gamma1 (z) ff N 0 (z) N (z) ff 1 N Gamma1 (z) ff N 0 (z) 5) Notice that ....

Cadzow J.A. Spectral estimation: An overdetermined rational model equation approach. Proc. IEEE, Vol. 70, pp. 907--939, 1982.

....the Yule Walker equations to determine the AR coefficients, it may be expected that the better the covariance estimates used, the more accurate the AR coefficient estimates yielded. We examine how the Capon covariance estimates can be used with the overdetermined modified YuleWalker (OMYW) method [6] [7] to compute more accurate AR coefficients. We find that the performances of the usage are critically dependent on the pole and zero locations and generally better AR coefficient estimates are obtained by using the Capon covariance estimates than by the standard ones. Another application ....

....method. 5. 2 AR Coefficient Estimation for ARMA Signals As an application of the Capon method for covariance estimation, we include here an example on how to use the Capon covariance estimates to find the AR coefficients of ARMA signals via the overdetermined modified Yule Walker (OMYW) method [6] [7] 8] We first briefly explain the OMYW method. For an ARMA(p; q) process, the covariance sequence and the AR coefficients are related by 2 6 6 6 6 6 6 6 6 6 6 4 r(q) r(q Gamma 1) Delta Delta Delta r(q Gamma p 1) r(q 1) r(q) Delta Delta Delta r(q Gamma p 2) ....

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J. A. Cadzow, "Spectral estimation: An overdetermined rational model equation approach," Proceedings of the IEEE, vol. 70, pp. 907--939, September 1982.

....order, the parsimonic order, to select the size of the Yule Walker problem. Otherwise one may end up having to deal with a rank deficient algebraic system, resulting in spurious spikes in the spectral estimate or loss of information due to a too small model order. It has been shown by Cadzow [4] that upon using more than the minimal number of equations (i.e. least squares problem) a reduction in data induced model parameterhypersensitivity is obtained and a corresponding improvement in modeling performance is then obtained. This is especially true for noisy environments and apply for ....

.... can most often be obtained by using the total least squares formulation [7] cf. 26, 12, 1] Moreover, further improvements can be obtained by using an extended order model and apply Singular Value Decomposition to reduce the rank of the obtained overdetermined, extended order matrix, e.g. [4, 25, 24]. This ideally allow for separation of noise and signal components. During the past decade much interest has been given to the application of SVD to such and other digital signal processing applications. SVD provides among things a tool for analyzing and solving rank deficient and or perturbed ....

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J. A. Cadzow. Spectral Estimation: An Overdetermined Rational Model Approach. Proceedings of the IEEE, 70(9), 1982.

.... back to potential theory in the work of Caratheodory, Toeplitz, and Schur [9, 10, 31, 30] and continuing in the work of Kalman, Georgiou, Kimura, and others [18, 14, 21] It has been of more recent interest due to its significant interface with problems in signal processing and speech processing [11, 8, 25, 20] and in stochastic realization theory and system identification [2, 32, 22] Indeed, the recent solution to this problem, which extended a result by Georgiou and confirmed one of his conjectures [13, 14] has shed some light on the stochastic (partial) realization problem through the development ....

....process y(t) is given by the Fourier expansion #(e i# ) # # # c k e ik# (2.1) on the unit circle, where the covariance lags c k = E y t k y t , k = 0, 1, 2, 2.2) play the role of the Fourier coe#cients c k = 1 2# # # # e ik# #(e i# )d#. 2. 3) In spectral estimation [8], identification [2, 22, 32] speech processing [11, 25, 24, 29] and several other applications in signal processing and systems and control, we are faced with the inverse problem of finding a spectral density which is coercive, i.e. positive on the unit circle, given only c = c 0 , c 1 , ....

<F3.754e+05> J. A.<F3.802e+05> Cadzow,<F4.133e+05> Spectral estimation: An overdetermined rational model equation<F3.802e+05> approach, Proc. IEEE, 70 (1982), pp. 907--939.

....841 2) This paper as well as further publications are available via anonymous ftp to abnt2.et2.tu harburg.de . 1. 2 Residual Time Series approach For the blind identification of possibly mixed phase ARMA systems, different Residual Time Series (RTS) procedures have been proposed in literature [1, 2]. Although the common basic idea is to separately estimate the AR and MA parameters of the channel model, the algorithms to sequentially identify the denominator and nominator of the rational model do vary. With the RTS scheme proposed in [3, 4] the AR estimation is geared to permit optimum MA ....

....parts like equivalent like equivalent allpass free ch. allpass free ch. Table 1: ACS cum. estimation error power and correlation 3 Blind AR identification 3. 1 Modified Yule Walker (mYW) eqns For AR parameter estimation of ARMA systems, the use of 2nd order modified Yule Walker (2mYW) equations [12, 1, 13, 14] is wide spread, where an additional time delay is introduced into the autocorrelation lags to account for the influence of the model s MA part. This is equivalent to shifting the autocorrelation estimates with lag zero from the main diagonal of the autocorrelation matrix to the q th diagonal, ....

J. A. Cadzow. Spectral Estimation: An Overdetermined Rational Model Equation Approach. Proceedings of the IEEE, 70(9):907-- 939, September 1982.

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Cadzow J A, Spectral Estimation: An Overdetermined Rational Model Equation Approach, Proc. IEEE, 1982, 70(9): 907--939.

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J. A. Cadzow, "Spectral Estimation: An Overdetermined Rational Model Approach," Proceedings of the IEEE, vol. 70, no. 9, 1982.

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