This paper addresses the problem of blind equalization for digital communications using an array of sensors at the receiver to copy constant modulus signals in the presence of heavy-tailed additive channel noise. First, we demonstrate the negative effects of channel noise to the original constant modulus algorithm (CMA) cost function in terms of convergence. Then, we introduce a new CMA criterion based on the fractional lower-order statistics (FLOS) of the received data. The proposed criterion is able to mitigate impulsive noise at the receiver and at the same time restores the constant modulus character of the transmitted communication signal. We perform an analytical study of the properties of the new cost function and we illustrate its convergence behavior through computer simulations.

This paper studies methods for space-time adaptive processing-based (STAP-based) parameter estimation in the presence of impulsive noise backgrounds. Towards this goal, the theory of alpha-stable random processes provides an elegant and mathematically tractable framework for the solution of the detection and parameter estimation problems in the presence of impulsive radar clutter. Our goal is to develop joint target angle and Doppler, maximum likelihood-based estimation techniques from radar measurements retrieved in the presence of severe clutter modeled as an alpha-stable, complex random process. We derive the Cramer-Rao bounds for the additive Cauchy interference scenario to assess the best-case estimation accuracy which can be achieved. The results are of great importance in the study of space-time adaptive processing (STAP) for airborne pulse Doppler radar arrays operating in impulsive interference environments.

The problem of co-channel interference is encountered when, along with the signal of interest (SOI), one or more interfering signal(s) are present in a common receiver. This paper is primarily concerned with the development of a new linear co-channel interference mitigation algorithm which estimates the SOI and the interfering signal from their superposition in the presence of additive noise. The methods are inspired by the reconstruction of the interference from the null space of the SOI. Once the null space of the SOI is determined, the interfering signal is reconstructed via a set of linear operations. The presented methodologies demonstrate low complexity while maintaining a superior performance.

New methods for time delay and frequency delay estimation are introduced based on the theory of alpha-stable distributions. It is shown that these methods are robust for both Gaussian and non-Gaussian impulsive noise environments. Their improved performance is clearly demonstrated with both computer generated data and actual radar clutter data.

We develop an new adaptive beamforming technique based on fractional lower-order moment theory. The proposed adaptive beamformer adjusts the array response to a desired signal while discriminating against impulsive interference modeled as a stable process. Simulation results show that the new technique performs better in localizing a target both in space and Doppler, and thus offers the potential for improved airborne radar performance in space-time adaptive processing (STAP) applications.

New methods for parameter estimation and blind system identification for impulsive signal environments are presented. The data are modeled as stable processes. First, methods for estimating the parameters (characteristic exponent and dispersion) of a symmetric stable distribution are presented. The fractional lower-order moments, both positive and negative order, and their applications are introduced. Then a new algorithm for blind channel identification based on fractional lower-order moments is proposed. The alpha-spectrum, a spectral representation for impulsive environments, is developed. Conditions for blind identifiability of nonminimum phase FIR channels are established using the properties of the Alpha-Spectrum.

There exist real world applications in which impulsive channels tend to produce large amplitude interferences more frequently than Gaussian channels. The stable law has been shown to successfully model noise over certain impulsive channels. The authors propose subspace-based methods for the direction-of-arrival estimation problem in impulsive noise environments. They define the covariation matrix of the array sensor outputs and show that eigendecomposition-based methods, such as the MUSIC algorithm, can be applied to the sample covariation matrix to extract the bearing information from the measurements.

We address the problem of estimation of the parameters of the symmetric, alpha-stable model for impulsive interference. We propose new estimators based on asymptotic extreme value theory, order statistics, and fractional lower-order moments, which can be computed fast and are, therefore, suitable for the design of real-time signal processing algorithms. The performance of the new estimators is evaluated theoretically and via Monte-Carlo simulation.

Derives the exact likelihood function for identification of the parameter of a MA(1) system from observation of its output when the input is an i.i.d. Cauchy sequence of unknown dispersion. Computer simulation illustrates the procedure.

This paper introduces a new adaptive blind equalization method, the Power Cepstrum and Tricoherence Equalization Algorithm (POTEA), based on second- and fourth-order statistics of the received sequence. The algorithm performs simultaneous identification and equalization of a nonminimum phase channel from its output only. Simulation results, with QAM signals, are presented to demonstrate the effectiveness of POTEA.

Impulsive noise bursts in communication systems are traditionally handled by incorporating in the receiver a limiter which clips the received signal before integration. An empirical justification for this procedure is that it generally causes the signal-to-noise ratio to increase. Recently, very accurate models of impulsive noise were presented, based on the theory of symmetric /spl alpha/-stable probability density functions. We examine the performance of optimum receivers, designed to detect signals embedded in impulsive noise which is modeled as an infinite variance symmetric /spl alpha/-stable process, and compare it against the performance of several suboptimum receivers. As a measure of receiver performance, we compute an asymptotic expression for the probability of error for each receiver and compare it to the probability of error calculated by extensive Monte-Carlo simulation.>

We propose the use of higher order statistics (HOS)-based methods to address the problem of image restoration. The restoration strategy is based on the fact that the phase information of the original image and its HOS are not distorted by some types of blurring. The difficulties associated with the combination of 2-D signals and their HOS are reduced by means of the Radon transform. Two methods that apply the weight-slice algorithm over the projections are developed. Simulation results illustrate the performance of the proposed methods.

This article studies the formulation of new members of the Cohen-Posch (1985) class of positive time-frequency energy distributions. Members of this class are always positive functionals and satisfy the marginal constraints. Therefore, they can be properly interpreted as distributions. We considered the minimization of cross-entropy measures with respect to different priors or "a priori" distributions and the case of no prior or maximum entropy, and concluded with the necessity to introduce new marginal constraints. New mixed in time and frequency constraints are derived based on a "direction invariance" criterion on the time-frequency plane that are directly related to the Fractional Fourier Transform. The implications of this new constrains in the positive class are analyzed from an information theoretic perspective. We conclude that the new constraints provide enough information to fully determine the resulting distribution and thus, no "a priori" distribution is necessary.>

Blind equalization of a communication channel is achieved by jointly estimating the deterministic channel coefficients and the random data sequence. The EM algorithm is used to determine the ML estimate of the channel. To implement the EM algorithm, one needs the MMSE estimate of the data sequence for the given estimate of the channel at each step. To reduce computational complexity, a suboptimum procedure is suggested for the MMSE estimation of the data. Preliminary simulations show that the proposed algorithm converges rapidly for a short length of data even when the channel has deep nulls.>

Non-Gaussian statistical signal processing is important when signals and/or noise deviate from the ideal Gaussian model. Stable distributions are among the most important non-Gaussian models. They share defining characteristics with the Gaussian distribution, such as the stability property and central limit theorems, and in fact include the Gaussian distribution as a limiting case. To help engineers better understand the stable models and develop methodologies for their applications in signal processing. A tutorial review of the basic characteristics of stable distributions and stable signal processing is presented. The emphasis is on the differences and similarities between stable signal processing methods based on fractional lower-order moments and Gaussian signal processing methods based on second-order moments.>

A general class of higher-order time-frequency representations, including Wigner higher-order spectra (WHOS), has been defined and studied recently as an extension of bilinear time-frequency distributions in terms of instantaneous higher-order moments of the signal. The analysis of mono- and multicomponent signals is considered using higher-order based time-frequency distributions. A computationally feasible implementation of the Wigner bispectrum and trispectrum (WHOS in the third and fourth order domain) is proposed considering one slice of the multifrequency space. The problem of cross-terms cancellation is addressed, and reduced interference distributions are defined as an extension of the Choi-Williams distribution.>

Nonlinear equalizers find use in communication applications where the channel distortion is too severe for a linear equalizer to handle. Because of their nonlinear capability and other attractive properties, neural networks have become appealing candidates for equalization problems. The application of neural networks to adaptive equalization problems is investigated. In particular, realization structures (MLP-I, MLP-II) of a multilayer perceptron (MLP) with a backpropagation training algorithm are introduced, and it is shown that they work well for both PAM and QAM signals of any constellation size (e.g., 4-PAM, 8-PAM, 16-QAM, and 64-QAM). It is demonstrated that both MLP structures outperform the least mean square (LMS)-based linear equalizer when channel distortions are nonlinear.>

Complex cepstrum techniques are applied to cross-bispectra in order to simultaneously reconstruct three independent finite-time signals, given the cross-bispectrum of the three signals only. The method is applied to simultaneously identify three systems via the cross-bispectrum of their outputs, knowing only the statistics of the input. A least-squares method is presented to estimate the cross-bicepstral parameters of the three signals simultaneously. The method is nonparametric and noniterative, assuming only that the signals (or impulse responses) are exponential, stable, and have no zeros on the unit circle. It takes full advantage of the two-dimensional nature of the bispectrum to reconstruct the three signals (or identify the three systems) simultaneously.>

The Wigner higher-order spectra (WHOS) are defined as extensions of the Wigner distribution (WD) to higher-order statistics domains. A general class of time-frequency higher-order spectra is also defined in terms of arbitrary higher-order moments of the signal as generalizations of the Cohen's general class of time-frequency representations. For signal processing applications, discrete time and frequency WHOS distributions are introduced and shown to be implemented with two fast-Fourier-transform-based algorithms. One application in which the Wigner bispectrum is applied for the detection of transient signals embedded in noise is presented. The Wigner bispectrum is compared with the WD and simulation results are given.>

The authors present a blind deconvolution scheme for the reconstruction of a signal that propagates in a multipath environment in the presence of additive zero-mean Gaussian noise. Two receivers are placed to record the transmitted signal convolved with a different channel for each receiver, embedded in noise. The recorded signals are transformed in the bicepstrum domain where the additive zero-mean Gaussian noise is suppressed, and then the differences of their minimum phase cepstra coefficients and the differences of their maximum phase cepstra coefficients are computed. These differences correspond to the Fourier phases of two FIR (finite impulse response) sequences that can be reconstructed out of phase information only, as long as the transmission channels are FIR and they have no zeros on the unit circle. The reconstruction of these sequences leads to the computation of the minimum and maximum phase cepstra coefficients of the two channels, and subsequently the cepstra coefficients of the transmitted signal can be computed and combined to reconstruct the signal itself.>

An adaptive blind equalization method is introduced for nonminimum phase communication channels. The method estimates the inverse channel impulse response, by using the complex cepstrum of the fourth-order cumulants (tricepstrum) of the synchronously sampled received signal. As such, the proposed adaptive method depends only on the statistics of the received sequence, and is capable of reconstructing separately both the minimum and maximum phase response of the channel. It is demonstrated, by means of extensive simulations, that the proposed tricepstrum-based equalization scheme performs well and outperforms other existing blind equalizers, at the expense of higher computational complexity.>

The authors introduce a novel approach for bicepstrum (i.e. cepstrum of the bispectrum) estimation that combines the use of second- and third-order statistics, and show application of this method to the problem of detecting and estimating the time delay between signals received at two spatially separated sensors together with noise, as well as to nonminimum phase system identification. The approach for time delay estimation is parametric, in the sense that it provides the time delay estimates directly and explicitly instead of examining the results of some reference functions. The performance of this method is demonstrated for different noise conditions and lengths of data. The performance is also compared to that of the least-squares method, which is based entirely on second-order statistics. It is shown that bicepstrum-based time delay estimation provides larger performance gain when the noise sources are Gaussian spatially correlated with unknown correlation function.>

An iterative algorithm for reconstructing a finite impulse response (FIR) signal from only the phase of its bispectrum is introduced. The algorithm is based on the key observation that the differences of the bicepstrum coefficients contain all the information concerning the phase of the signal, whereas their sums contain the magnitude information. Analysis and simulation examples are presented to demonstrate the algorithm's convergence properties. It is also demonstrated that imposing an energy constraint causes the convergence rate of the algorithm to improve dramatically.>

An adaptive filtering method is proposed for the identification of a non-Gaussian, white-noise-driven, linear, generally non-minimum-phase system. The non-minimum-phase impulse response of the system is estimated from the updated differential cepstrum parameters of the higher order cumulants (polycepstra) of the system output. The updated cepstrum parameters are obtained by utilizing higher order cumulants and an LMS (least mean squares) type algorithm. It is shown, using Monte-Carlo simulation examples, that the proposed method would perform very well at the expense of more computations. The use and effectiveness of the method in blind linear-equalization applications is demonstrated.>

The purpose of this study is to present an analytic performance evaluation of the complex cepstrum and bicepstrum (i.e. cepstrum of the bispectrum) methods by providing explicit expressions of the bias and variance of cepstrum parameters. A model consisting of a deterministic signal in additive white Gaussian noise and finite length data is assumed. The authors compare a special case of these results and find the range of SNR in which they expect the bicepstrum method to perform better than the complex cepstrum method.>

A novel discrete-time method is proposed for estimating the impulse response of a frequency-selective digitally modulated communication channel. The received signal is first demodulated and sampled and then the fourth-order cumulants of the resulting discrete-time sequence are estimated. The method estimates the channel impulse response from the complex cepstrum of the aforementioned fourth-order cumulants (i.e. tricepstrum). The method depends only on the second- and fourth-order statistics of the transmitted sequence and is capable of reconstructing nonminimum-phase impulse responses. Monte Carlo simulation results demonstrate the effectiveness of the method, its low sensitivity to observation noise, and its improved performance in terms of probability of error or the reconstructed transmitted sequence.>

A novel adaptive identification scheme is introduced for a nonGaussian white-noise-driven linear, nonminimum-phase FIR (finite-impulse response) system. The adaptive scheme is based on noncausal autoregressive (AR) modeling of higher-order cumulants of the system output. In particular, the magnitude and phase response estimates at each iteration are expressed in terms of the updated parameters of the noncausal AR model. The set of updated AR parameters is obtained by using the LMS (least-mean-squares) algorithm and by using higher-order cumulants instead of time samples of the output signal. It is demonstrated by means of standard examples that the new adaptive scheme works well and, as expected, outperforms the modified (autocorrelation-based) LMS algorithm for nonminimum-phase system identification.>

A class of methods that estimate the difference in arrival time between two signals corrupted by spatially correlated Gaussian noise sources of unknown cross correlation is presented. The methods are based on the idea of comparing the similarities between the two sensor measurements in higher-order spectrum domains (bispectrum) rather than in the cross-correlation domain. It is demonstrated that the time delay estimation techniques based on higher-order spectra suppress the effect of correlated Gaussian noise sources and therefore exhibit improved performance over generalized cross-correlation methods. Studies are shown for different lengths of data records and signal-to-noise ratios.>

The authors address the bearing estimation problem of sources from array data (snapshots) in the presence of Gaussian color (spatially correlated) noises of unknown autocorrelation matrix. They demonstrate that the harmonic decomposition methods (signal and noise subspace) can easily be reformulated using fourth-order cumulant matrices instead of autocorrelations. Simulation results are presented and comparisons are made to show that the performance of the fourth-order cumulant-based methods (beamforming, MUSIC) is superior to that of their equivalent autocorrelation-based methods when the additive noise sources are colored Gaussian with unknown correlation matrix.>

A method is introduced for transient signal reconstruction based on bispectrum estimation techniques. The third-order cumulants of the noisy observation data are estimated first and an autoregressive model is then fitted in the sense of perfect matching between the third-order cumulant sequence of the model's impulse response and the estimated cumulants of the observation. It is demonstrated that the method is capable of reconstructing transient signals for environments in which the noise is color Gaussian with unknown autocorrelation function. >

The authors address the problem in which time delays are closely-spaced, i.e. the distance between two consecutive time delays is significantly less than the duration of the autocorrelation of the FM signal. A high-resolution estimation method using the cumulant cepstra (polycepstra) of the received sensor data as the basic tool for reconstruction is introduced. The effectiveness of the method is demonstrated for different noise conditions and lengths of data. The results apply to sonar signal processing problems in which the acoustic FM signal is embedded in reverberation noise due to the presence of multipath and observation noise.>

There are many significant applications of nonlinear adaptive digital filters such as the cancellation of echoes and intersymbol interference, the equalization of transmission channels, adaptive noise cancellation and design of optimal predictors in communication systems. In this paper, we introduce a class of efficient architectures for adaptive quadratic digital filters based on the LMS algorithm and on rank compressed lower-upper (LU) triangular decomposition method. The architectures exhibit high parallelism as well as modularity and regularity. They are mapped into parallel pipeline and systolic array implementations and are evaluated on hardware cost (in bits), and data throughput delay.

In this paper we propose a new method for non-minimum phase wavelet estimation and deconvolution based on non-causal autoregressive (AR) modeling of third moments of the output seismic trace. The magnitude and phase response of the wavelet are expressed in terms of the parameters of the noncausal AR model. The set of the AR parameters is obtained by solving an overdetermined linear system of equations which is formed using third moment estimates of the output data. A comparison of the non-causal AR bispectrum approach against more conventional approaches for wavelet magnitude and phase reconstruction is a major component of the paper. It is demonstrated by means of standard example that the proposed procedure achieves improved performance.

A new computationally efficient identification procedure is proposed for a non-Gaussian white noise driven linear, time-invariant, non-minimum phase system. The method is based on the idea of computing the complex cepstrum of higher-order cumulants of the system output. In particular, the differential cepstrum parameters of the system's impulse response are computed directly from higher-order cumulants via least-squares solution. The method is flexible enough to reconstruct the minimum and maximum phase components of the impulse response of MA, AR or ARMA systems without any prior knowledge of the type of the system. It does not require model order selection criteria and is shown to provide estimates with small bias and variance even with "short" length data records.

Most power spectrum estimation methods such as Pisarenko, Maximum Entropy, and conventional methods, assume that the given correlation functions are uniformly sampled in location. The situation where correlation functions are uniformly sampled but with uncertainty in their sample location has been overlooked by the spectrum estimation community. In this paper, the effects upon spectrum estimates are derived when there is location uncertainty in the correlation functions. To alleviate these effects, a modified approach that takes into account the uncertainty is developed. Simulation examples are given to demonstrate the uncertainty effects and to justify the improvements gained by using the new approach.

It is the purpose of this tutorial paper to place bispectrum estimation in a digital signal processing framework in order to aid engineers in grasping the utility of the available bispectrum estimation techniques, to discuss application problems that can directly benefit from the use of the bispectrum, and to motivate research in this area. Three general reasons are behind the use of bispectrum in signal processing and are addressed in the paper: to extract information due to deviations from normality, to estimate the phase of parametric signals, and to detect and characterize the properties of nonlinear mechanisms that generate time series.

A family of autoregressive (AR) detection statistics is introduced and their potential for enhanced detection of unknown-frequency sinusoids in noise is illustrated. AR models applied to both the time data and the correlation data are addressed and compared. The computational complexity of the resulting decision rules is also incorporated in the analysis.

A new approach is introduced for the exact decomposition of a 2-d IIR digital fitler into a set of parallel filters plus a set of parallel blocks of multiply-in, add-out type of operations. It is shown that the adopted decomposition approach yields a general realization scheme of high parallelism and simple replicated hardware. It is also demonstrated that the new structure achieves much less data throughput delay per output sample than the block realization. Procedures for obtaining various other optimal realizations are discussed.

A sufficient condition for the extendibility of two-dimensional (2-d) quadratically symmetric autocorrelation samples is derived based on matrix decomposition approaches. This condition is very simple to test because it boils down to a positive definiteness checking of a set of Toeplitz form matrices. It is shown by means of examples that this sufficient condition can be very useful, in some cases, by making the tedious extendibility test unnecessary. This paper also presents a method which can approximate with small error a given quadratically symmetric autocorrelation function (a.c.f) over a square with a new a.c.f that is guaranteed to be extendible. This method is also based on a matrix decomposition approach and employs an iterative gradient algorithm. Its implications to the estimation of a 2-d power spectrum is demonstrated.

A new method for multichannel autoregressive (AR) spectrum estimation is introduced based on an iterative gradient algorithm. In the context of Dynamic Programming, the method is shown to be optimum in reflection coefficient domain, whereas existing multichannel AR methods such as the Nuttall-Strand algorithm, are shown to be suboptimum. It is demonstrated that the drawbacks of the Nuttall-Strand method, namely frequency bias and line-splitting in processing sinusoidal signals, are eliminated by the optimum approach. However, the improved performance is achieved at the expense of considerably more computational effort and time.

Bispectrum estimation has been used to detect quadratic phase coupling among sinusoids in noise, in phase measurements for non-Gaussian processes, system identification etc. Most of the known estimation methods belong to the 'conventional' or 'Fourier-type' class. Recently, a parametric approach was proposed. All known methods perform poorly in terms of resolution when the given data records are short. The Constrained Third Order Mean (CTOM) method proposed in this paper estimates the parameters of an autoregressive (AR) model driven by non-Gaussian white Noise (NGWN) by setting the sample mean of the Third Order Recursion (TOR) error process to zero. The resulting bispectrum estimates perform very well in detecting quadratic phase coupling when the data records are short.

In this paper a new stable modification of the weighted Burg technique for autoregressive (AR) spectral estimation is introduced based on data-adaptive weights that are proportional to the common power of the forward and backward AR process realizations. It is shown that AR spectra of short length sinusoidal signals generated by the new approach do not exhibit phase dependence or line-splitting. Further, it is demonstrated that improvements in resolution may be so obtained relative to other weighted Burg algorithms. The method suggested here is shown to resolve two closely-spaced peaks of dynamic range 24 dB whereas the modified Burg schemes employing rectangular, Hamming or "optimum" parabolic windows fail.

In the paper a new method is introduced for the exact decomposition of a linear Mth-order periodically time-varying digital filter into a set of independent linear Mth-order time-invariant digital filters, each one of which is a single-input, multiple-output system. It is shown that the adopted decomposition approach yields to a general realization scheme that exhibits high parallelism as well as great modularity and regularity. Procedures for obtaining various optimal realizations are discussed and the application of the decomposition method to the realization of linear time-invariant digital filters is examined.

Higher order spectra provide information about processes not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality. The bispectrum which is a third order spectrum provides information about quadratic phase coupling among harmonic components. Bispectrum estimation has been applied in diverse fields principally to obtain such information. Existing methods for bispectrum estimation are patterned after the conventional methods for power spectrum estimation which are known to possess certain limitations. The paper proposes a parametric approach to bispectrum estimation based on AR modeling of time series. The definition and properties of a parametric bispectrum estimator in the general ARMA case are stated. The third moment recursion equations that follow from the model assumptions for the proposed AR bispectrum estimator are presented. The estimates are derived using biased estimates of the third moments in these equations. Results from preliminary experiments suggest that the resulting method does possess certain attractive features when compared with existing methods.

A new approach to the realization of two-dimensional (2-d) FIR and IIR digital filters is introduced based on the so-called "Lower-Upper triangular (LU) decomposition" of matrix coefficients of their two-dimensional polynomials. It is shown that a general two-dimensional transfer function can be exactly realized in terms of polynomials of order one, each one of which is a function of one of the two space variables only. It is demonstrated that the LU realization scheme exhibits high inherent parallelism as well as great modularity, regularity and flexibility. This paper also shows that the computational requirements of the LU realization are much less than these of the Jordan (J), Singular Value (SV) and canonical realization schemes.

A new class of multi-dimensional (m-D,m=3,4) spectral estimation algorithms is introduced based on the minimum variance representations (MVR) of m-D (m=3,4) data fields. These representations are defined in the framework of linear prediction where it is shown that they may be classed into general categories depending upon the geometry of the prediction space. For example, in the 3-D case it is shown that there are four possible models: causal, semicausal I, semicausal II, and non-causal. The m-D (m=3,4) model formalisms and their linear-predictive and spectral interpretations are derived. The admissibility conditions of the spectral density function are also discussed. To obtain high-resolution spectral estimates from finite length m-D (m=3,4) data fields, the models are fitted to the data optimally in the sense of minimizing the covariance recursion errors within the prediction space considered. Computer-simulated short data fields consisting of two travelling waves embedded in noise are employed to demonstrate experimentally that the class of algorithms developed in this paper improves on the standard techniques for high-resolution and robustness in the presence of nonstationarities, such as envelope modulation.

A new method for generating the AR process parameters useful for spectral estimation is introduced. The method is based on weighted averaging of forward and backward models with weights proportional to the corresponding average energies of the linear prediction errors. It is demonstrated that improvements in resolution may be so obtained relative to equally weighted forward-backward schemes. It is also shown that this method results in asymptotically consistent estimates for stationary data and in the nonstationary case bounds the influence of the poorer of the forward-backward models. Finally, it is demonstrated that the new technique permits recursive implementation with computational complexity proportional to the AR process order squared.

A new algorithm of 2-D spectral estimation is introduced based on unconstrained minimization of the estimated covariance recursion error of the Minimum Variance Models (causal, semicausal, noncausal). The model parameters are estimated directly from the data field in a manner which combines high resolution with robustness in the presence of nonstationarities. Computer-simulated short data fields consisting of two closely spaced travelling waves are employed to demonstrate that the method developed in this paper improves on the standard techniques for high resolution. The application of the new algorithm in intramyocardial data taken from ischemic and hypothermic intact canine preparations is also demonstrated. It is shown that by using this technique, the number and velocity vector of cardiac propagating wavefronts may be reliably determined, though the sets of cardiac data are very short and highly nonstationary. The clinical significance in evaluating prearrhythmic states of the heart and predicting onset of manifest arrhythmias is also discussed.

A new method of AR parameter estimation for maximum entropy spectral estimation is introduced using forward and backward optimal linear predictors weighted by the forward and backward process realization energies, respectively. AR parameters estimated by this Energy-Weighted (EW) method are constrained to satisfy the fast Levinson recursion. The reflection coefficients of each stage are computed from the harmonic mean of the same-stage energy weighted forward and backward reflection coefficients. AR spectra generated by the EW method are shown to have improved performance over AR spectra generated by the Burg algorithm. These improvements include sharper resolution, less frequency bias, less phase dependence, less noise spectral variance and absence of spectral line splitting. The EW method has the simplicity and the computational efficiency of the Burg Algorithm.

In this paper a new filter structure that allows precise pole realization at a variety of locations inside the unit circle is developed and its performance investigated. The proposed structure is based on the ides of augmenting the system to a higher order unobservable filter whose poles are obtained precisely while keeping the multipliers realizable within the given word-length. The additional undesirable poles that result from this augmentation are cancelled approximately by zeros. This results from the fact that the poles are precise and the perturbation is confined to the zeros while the minimal order filter suffers from perturbation of its poles. The unobservable structure is of particular significance for poles either near or on the unit circle where sensitivity to perturbation is high.