Burg's Maximum Entropy Method Research Articles

Optical Spectrum Analysis of Real-Time TDDFT Using the Maximum Entropy Method

In the calculation of time-dependent density-functional theory in real time, we apply an external field to perturb the optimized electronic structure, and follow the time evolution of the dipole moment to calculate the oscillator strength distribution. We solve the time-dependent equation of motion, keeping track of the dipole moment as time-series data. We adopt Burg's maximum entropy method (MEM) to compute the spectrum of the oscillator strength, and apply this technique to several molecules. We find that MEM provides the oscillator strength distribution at high resolution even with a half of the evolution time of a simple FFT of the dynamic dipole moment. In this paper we show the effectiveness and efficiency of MEM in comparison with that of FFT. Not only the total number of time steps, but also the length of the autocorrelation, the lag, plays an important role in improving the resolution of the spectrum.

Complexity in the high latitude HF radar spectral width boundary region

Abstract. SuperDARN radars are sensitive to the collective Doppler characteristics of decametre-scale irregularities in the high latitude ionosphere. The radars routinely observe a distinct transition from large spectral width (>100 m s−1) located at higher latitudes to low spectral width (<50 m s−1) located at lower latitudes. Because of its equatorward location, the TIGER Tasmanian radar is very sensitive to the detection of the spectral width boundary (SWB) in the nightside auroral ionosphere. An analysis of the line-of-sight velocities and 2-D beam-swinging vectors suggests the meso-scale (~100 km) convection is more erratic in the high spectral width region, but slower and more homogeneous in the low spectral width region. The radar autocorrelation functions are better modelled using Lorentzian Doppler spectra in the high spectral width region, and Gaussian Doppler spectra in the low spectral width region. However, paradoxically, Gaussian Doppler spectra are associated with the largest spectral widths. Application of the Burg maximum entropy method suggests the occurrence of double-peaked Doppler spectra is greater in the high spectral width region, implying the small-scale (~10 km) velocity fluctuations are more intense above the SWB. These observations combined with collective wave scattering theory imply there is a transition from a fast flowing, turbulent plasma with a correlation length of velocity fluctuations less than the scattering wavelength, to a slower moving plasma with a correlation length greater than the scattering wavelength. Peak scaling and structure function analysis of fluctuations in the SWB itself reveals approximately scale-free behaviour across temporal scales of ~10 s to ~34 min. Preliminary scaling exponents for these fluctuations, αGSF=0.18±0.02 and αGSF=0.09±0.01, are even smaller than that expected for MHD turbulence.

Classification of cardiac arrhythmias using fuzzy ARTMAP.

We have investigated the QRS complex, extracted from electrocardiogram (ECG) data, using fuzzy adaptive resonance theory mapping (ARTMAP) to classify cardiac arrhythmias. Two different conditions have been analyzed: normal and abnormal premature ventricular contraction (PVC). Based on MIT/BIH database annotations, cardiac beats for normal and abnormal QRS complexes were extracted from this database, scaled, and Hamming windowed, after bandpass filtering, to yield a sequence of 100 samples for each ORS segment. From each of these sequences, two linear predictive coding (LPC) coefficients were generated using Burg's maximum entropy method. The two LPC coefficients, along with the mean-square value of the QRS complex segment, were utilized as features for each condition to train and test a fuzzy ARTMAP neural network for classification of normal and abnormal PVC conditions. The test results show that the fuzzy ARTMAP neural network can classify cardiac arrhythmias with greater than 99% specificity and 97% sensitivity.

In Vivo potassium-39 NMR spectra by the burg maximum-entropy method

The Burg maximum-entropy method was applied to estimate 39K NMR spectra of mung bean root tips. The maximum-entropy spectra have as good a linearity between peak areas and potassium concentrations as those obtained by fast Fourier transform and give a better estimation of intracellular potassium concentrations. Therefore potassium uptake and loss processes of mung bean root tips are shown to be more clearly traced by the maximum-entropy method.

ESPRIT--Estimation of Signal Parameters via Rotational Invariance Techniques

High-resolution signal parameter estimation is a problem of significance in many signal processing applications. Such applications indude direction-of-arrival estimation, system identification, and time series analysis. A novel approach to the general problem of signal parameter estimation is described. Although discussed in the context of directionof- arrival estimation, ESPRIT can be applied to a wide variety of problems. It exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure. The technique, when applicable, manifests significant performance and computational advantages over previous algorithms such as Burg's maximum entropy method, Capon's maximum likelihood method, and Schmidt's multiple signal classification.

Approximation–Theoretic Derivation of Logarithmic Entropy Principles for Inverse Problems and Unique Extension of the Maximum Entropy Method to Incorporate Prior Knowledge

The minimum distance approach for reconstructing a positive function based on knowledge of finitely many linear functional values is examined. Two important classes of directed distances for signal processing and statistical inference are discussed. By imposing conditions analogous to those satisfied by linear projections in Hilbert space, two logarithmic entropy principles are derived. One of these involves the Itakura–Saito distortion measure of communication theory and uniquely extends Burg's maximum entropy method to incorporate prior knowledge. The other uses the Kullback–Leibler distance of statistics.

Maximum entropy spectral analysis of NMR signals of solids

The Burg maximum entropy method and the LPSVD modeling method have been applied to solid-state spectra. The Burg method is suitable for determining the positions of lines and the Barkhuijsen method seems to be appropriate for the determination of amplitudes and linewidths.

Linear prediction z-transform (LPZ) method, Padé rational approximation, and the burg maximum entropy extrapolation

Alternatives to fast Fourier transformation using the linear prediction z-transform method and the Padé rational approximation method are discussed. These two closely related methods can be used to obtain a phase-sensitive spectrum with enhanced spectral resolution and reduced noise. Similarities and differences between the Burg maximum entropy method and the linear prediction extrapolation are discussed.

Simulation of nonstationary spectral analysis of turbulence in the aorta using a modified autoregressive or maximum entropy (AR/ME) method.

A new method of parametric spectral calculation based on the ensemble average technique, which is a natural expansion of the Burg's maximum entropy method, is proposed. This method is applied to a set of numerical simulation data which simulate turbulent velocity fluctuations data measured in the canine aorta with a hot-film anemometer. The autoregressive order of the spectral calculation is chosen by the minimum AIC (Akaike's information criteria) method. It is shown that the proposed method used with the minimum AIC method has a very good performance calculating smooth averaged spectra in the short-time quasisteady spectral analysis of nonstationary processes such as turbulence in the aorta.

High‐resolution beamforming with oversampled arrays

Plane‐wave beamforming is interpretable as estimation of the Fourier wave vector spectrum from samples of the spatially dependent acoustic field. Because spatially localized sources contribute discrete peaks to the wave vector spectrum, the use of high‐resolution nonlinear techniques (such as Burg's maximum entropy method—MEM) to resolve closely spaced sources has received much attention [Johnson, Proc. IEEE 70(9), 1018–1028 (1982)]. Such techniques are expected to be most useful for short arrays, whose dimensions do not exceed a few wavelengths, for which case conventional beamforming offers poor resolution. Such short arrays typically contain a number of hydrophones and thus oversample the spatial field; the spacing between adjacent hydrophones is less than one half a wavelength. When MEM is applied to oversampled arrays, spurious features are often produced due to the concentration of the spectrum within the visible region of wave vectors. These spurious features can be eliminated through the use of a more general high resolution procedure, the weighted reciprocal spectrum approximation method [Byrne and Fitzgerald, IEEE Trans. Acoust. Speech Signal Process. ASSP‐31, 276–279 (1983)].

Simulation experiments to compare the signal detection properties of DFT and MEM spectra

Four simulation experiments have been carried out to compare the statistics of threshold detection of a complex sinusoid in additive noise using the Burg maximum entropy method (MEM) and the discrete Fourier transform (DFT) technique. The results indicate that, in the presence of additive white noise, the DFT consistently provides a higher signal detection probability P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> and a more accurate estimate of signal frequency than the MEM. In the presence of colored noise, the DFT provides a higher P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> when signal-to-noise ratio (SNR) is high, or when signal detection is carried out in the low false-alarm probability P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</inf> region. Only in the very restricted case of low SNR together with a high P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FA</inf> and the signal far away from the center of the noise band does the MEM provide a higher P <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> than the DFT.

Estimation of Short-Time Spectral Envelope of Voiced Speech Using Maximum Entropy Method of Spectral Analysis

The Burg maximum-entropy (ME) method of spectral analysis is used to estimate the short-time spectral envelope of the voiced speech-signal. A number of vowel segments from continuous speech are analysed using this method. The Burg ME method is compared with the autocorrelation and covariance methods of linear prediction using normalized linear prediction error and accuracy in estimating the speech spectrum as criteria. The results obtained from pitch-synchronous and pitch-asynchronous analysis of vowel segments are discussed.

Spectral analysis and adaptive array superresolution techniques

Recent nonlinear techniques reported in the field of spectral analysis are of great interest in other fields as well, including radio-frequency (RF) adaptive array antenna systems. This paper is primarily a cross-fertilization treatise which takes the two most popular nonlinear techniques, the Burg maximum entropy method and the maximum likelihood method, and relates them to their similar nonlinear adaptive array antenna counterparts, which consist of the generic sidelobe canceller and directional gain constraint techniques. The comparison analysis permits an examination of their principles of operation from the antenna spatial pattern viewpoint, and helps to qualify, their actual superresolution performance. A summary of the resolution performance of several adaptive algorithms against multiple-incoherent sources is provided, including a universal graph of signal-to-noise ratio (SNR) versus source separation in beamwidths for the case of two equal-strength sources. Also, a significant dividend in the easy resolution of unequal-strength sources is reported. The superresolution of coherent spatial sources or radar targets is more difficult for these techniques, but successful results have been obtained whenever sufficient relative motion or Doppler cycles are available. Two alternate adaptive spatial spectrum estimators are suggested, consisting of a circular array predicting to its center point, and a new thermal noise algorithm.

Estimation of short-time spectral envelope of voiced speech using maximum entropy method of spectral analysis

The Burg maximum entropy (ME) method of spectral analysis is used to estimate the short-time spectral envelope of the voiced speech signal. A number of vowel segments from continuous speech are analyzed using this method. The Burg ME method is compared with the autocorrelation and covariance methods of linear prediction using normalized linear prediction error and accuracy in estimating the speech spectrum as criteria. It is shown that the Burg ME method consistently gives better results than the autocorrelation method of linear prediction for both pitch-synchronous and pitch-asynchronous analyses. For pitch-synchronous analysis, this method performs slightly better than the covariance method, while for pitch-asynchronous analysis, its performance is marginally inferior to that of the covariance method.

ON WIENER FILTER AND MAXIMUM ENTROPY METHOD FOR MULTICHANNEL COMPLEX SYSTEMS*

AbstractThe Wiener filtering scheme is obtained for a multichannel complex system utilizing the “block‐Toeplitz” property of autocorrelation matrix. A numerical example is given to elucidate the application of the filter design. The study also outlines Burg's maximum entropy method to include the multi‐channel complex realm.

A comparison between burg's maximum entropy method and a nonrecursive technique for the spectral analysis of deterministic signals

It is demonstrated that the anomalous behavior of the Burg method on processing sinusoids is due to the Toeplitz structure inherent in the derivation of the recursion algorithm. A straightforward non‐recursive approach is described which (for sinusoids) not only is shown to be free of these anomalies but also seems to offer superior noise performance.

Spectral line similarity in the geomagnetic dipole field variations and length of day fluctuations

Power spectral density analysis using Burg's maximum entropy method (MEM) was applied to the geomagnetic dipole field and its rate of change for the years 1901-1969. Both spectra indicate relative maxima at 0.015 cycle/yr and its harmonics. These maxima correspond approximately to 66-, 33-, 22-, 17-, 13-, 11-, and 9-year spectral lines. The application of the same analysis techniques to the length of day (l.o.d.) fluctuations for the period 1865-1961 reveals similar spectral characteristics. The existence of the common spectral peaks with periods of 66 and 33 years in the l.o.d. fluctuations and the geomagnetic dipole field is clearly established. The existence of the higher harmonics is somewhat uncertain because of the line-splitting problem in the MEM spectral analysis. It is suggested that the spectral line similarity in the l.o.d. fluctuations and the dipole field variations is related to the motion within the earth's fluid core during the past 100 years.

Spectral analysis of paleomagnetic time series

Spectral analysis of paleomagnetic directions can be accomplished easily by first mapping the data onto the complex plane and then using a reliable spectral estimator such as Burg's maximum entropy method for complex time series. Paleomagnetic measurements on the Narita bed by Nagata et al. serve to illustrate the procedure. Spectra of paleosecular variation are helpful for resolving historical tendencies toward clockwise and counterclockwise field motions associated with nondipole longitudinal drift.