Propane spectral resolution enhancement by the maximum entropy method

This paper analyzes algorithms which are suitable for spectral estimates of noisy signals in the frequency domain based on the use of the fast Fourier transform (FFT). Several causes of inaccuracy are analyzed and characterized so that the expressions of different components of error on the power spectral density (psd) estimate are given, in terms both of spectral properties of noise and typical parameters of the used filter. These simple expressions point out how an appropriate choice of some window parameters may increase considerably the accuracy of the estimate. The effects of choice on the accuracy are examined. In any case, the performance of the psd estimator can be improved by adopting linear or nonlinear averaging techniques; in the paper the statistical properties of geometric mean of periodograms are particularly examined and compared with those of the more traditional Welch's method. It is proved that, under appropriate conditions, the geometric mean produces a reduction both of bias and variance of psd. Numerical simulations confirm these theoretical results.

Broken rotor bars in an induction motor create asymmetries and result in abnormal amplitude of the sidebands around the fundamental supply frequency and its harmonics. Applying a spectrum analysis technique on motor current and inspecting the spectrum amplitudes at the broken rotor bar specific frequencies for abnormality is a well-known procedure for broken rotor bar fault detection and diagnosis. Among the spectrum analysis techniques for broken rotor bar fault detection, the fast Fourier transform (FFT) is the most widely used technique. There are other spectrum techniques, which are based on the power spectral density estimates. In this paper we compare the three well-known spectrum analysis methods: FFT, periodogram and Welch's periodogram methods according to their performance on the broken rotor bar fault detection problem. The results indicate that Welch's periodogram method has better fault discrimination capability and is more robust compared to the other two methods. A statistical hypothesis test applied to the results of the three methods depicts the comparison results quantitatively.

Some problems in the spectral analysis of human stabilograms are discussed. Power spectra were computed by the following three methods ; fast Fourier transform (FFT) method, autoregressive (AR) models and maximum entropy method (MEM). Power spectra were obtained from original time series (original waves) or separately from the high-pass filtered component (cut-off frequency 0.15 Hz).A distribution of the power spectra did not reveal any dominant frequency in original waves. The spectra derived from the high-pass filtered component revealed peaks in the majority of cases. It was essential for analyzing the power spectra to cut the lower frequency band from the original waves.FFT spectra showed large variance and high oscillation. Therefore, it was difficult to detect the dominant frequency. AR and MEM spectra showed stable and smooth spectral curves. Furthermore, since the influence of past sways were taken into account in AR models and the MEM method, these two methods were superior for the detection of periodicity of body sways.

We present an extension to Jaynes’ maximum entropy principle that incorporates latent variables. The principle oflatent maximum entropywe propose is different from both Jaynes’ maximum entropy principle and maximum likelihood estimation, but can yield better estimates in the presence of hidden variables and limited training data. We first show that solving for a latent maximum entropy model poses a hard nonlinear constrained optimization problem in general. However, we then show that feasible solutions to this problem can be obtained efficiently for the special case of log-linear models---which forms the basis for an efficient approximation to the latent maximum entropy principle. We derive an algorithm that combines expectation-maximization with iterative scaling to produce feasible log-linear solutions. This algorithm can be interpreted as an alternating minimization algorithm in the information divergence, and reveals an intimate connection between the latent maximum entropy and maximum likelihood principles. To select a final model, we generate a series of feasible candidates, calculate the entropy of each, and choose the model that attains the highest entropy. Our experimental results show that estimation based on the latent maximum entropy principle generally gives better results than maximum likelihood when estimating latent variable models on small observed data samples.

Maximum entropy method spectral estimation applied to power cable diagnostics via cepstrum processing

The modeling of complex service systems entails capturing many sub-components of the system, and the dependencies that exist among them in the form of a joint probability distribution. Two common methods for constructing joint probability distributions from experts using partial information include maximum entropy methods and copula methods. In this paper we explore the performance of these methods in capturing the dependence between random variables using correlation coefficients and lower-order pairwise assessments. We focus on the case of discrete random variables, and compare the performance of these methods using a Monte Carlo simulation when the variables exhibit both independence and non-linear dependence structures. We show that the maximum entropy method with correlation coefficients and the Gaussian copula method perform similarly, while the maximum entropy method with pairwise assessments performs better particularly when the variables exhibit non-linear dependence.

Radix-2 based fast Fourier transform (FFT) routines have been the main stream FFT that are commonly applied to the measurement and analysis of electric power system data. Because of the rigid sampling rates offered by most of the instrument manufacturers and the mathematical limitation imposed by the algorithm of radix-2 FFT, artificial post sampling data windows have been introduced to improve the utility of the radix-2 FFT. The 60 Hz and the 50 Hz based electrical power system frequencies are incompatible with the radix-2 FFT. There has been an ongoing search to adapt the FFT routine to the special requirements of electric power systems. Advances in the personal computer hardware has opened a new approach to perform the FFT via mixed radix routines. It offers greatly improved flexibility in the selection of a practical data size. This leads to the elimination of the need of the post sampling software windows. It also allows one to relax or eliminate the requirement of anti-aliasing measures for power system harmonic measurements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nature, wavefield properties and source mechanism of volcanic tremor: a review

On the interpretation of the electrochemical noise data for coatings

With a view to developing efficient methodologies for the evaluation of the asymmetry parameter of the electric field gradient (EFG) tensor from polycrystalline specimens, an alternative approach which involves two‐dimensional spin‐echo NQR data processing by the maximum entropy method (MEM) is presented. The superiority of MEM over the traditional fast Fourier transform (FFT) method is demonstrated by the analysis of two‐dimensional NQR data obtained using the modified pulse sequence. The method has been successfully applied to the determination of the EFG tensor at the 75As site in the antiferroelectric phase of polycrystalline ammonium dihydrogenarsenate (ADA), where conventional nutation spectroscopy fails owing to the large NQR linewidth.

Two-dimensional nutation FT/MEM 35Cl nuclear quadrupole resonance spectroscopy and hydrogen bonding in 2,6-dichlorophenol

Interferometric instruments have the following serious weak points: (1) the necessity of doing a Fourier transform that involves a vast amount of calculation; (2) the lack of knowledge of suitable measuring conditions until the Fourier transform is finished; and (3) the spectral resolution of the conventional Fourier-based techniques is significantly affected by the sampling rate, data length, and noise in signal processing. In this paper, an enhanced spectrometer is proposed using the modified forward-backward linear prediction method (MFBLP) with a search algorithm. To document the advantage of the method presented, a computer simulation for multiple-wavenumber estimation is investigated. The MFBLP method is truly superior to the fast Fourier transform (FFT) method. In general, the spectral resolution using the FFT method is proportional to the data length. In this paper, however, it is shown that excellent results can also be obtained from only 60 sample points using the FFT method. Moreover, from experimental results, we also conclude that the sampling rate must be consistent with the condition 632<f/sub p//spl middot/t/spl middot/D<3164, where f/sub p/, represents the value of the pulse generator frequency in Hz, t the observation time, and D the decimation factor.

A slow-scan "real-time" Michelson interferometer and a new rapid-scan interferometer using signal averaging techniques and fast Fourier transform (FFT) spectrum computation are described and compared. Typical performances of both instruments are illustrated.

Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

Speech recognition is becoming popular in current development on mobile devices. Presumably, mobile devices have limited computational power, memory size and battery life. In general, speech recognition is a heavy process that required large sample data within each window. Fast Fourier Transform (FFT) is the most popular transform in speech recognition. In addition, FFT operates in complex field with imaginary numbers. This paper proposes an approach based on discrete orthonormal Tchebichef polynomials as a possible alternative to FFT. Discrete Tchebichef Transform (DTT) shall be utilized here instead of FFT. The preliminary experimental result shows that speech recognition using DTT produces a simpler and efficient transformation for speech recognition. The frequency formants using FFT and DTT have been compared. The result showed that, they have produced relatively identical output in term of basic vowel and consonant recognition. DTT has the potential to provide simpler computing with DTT coefficient real numbers only than FFT on speech recognition.