Confidence intervals for the maximum entropy spectrum

A neural net algorithm for multidimensional maximum entropy spectrum estimation

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.

Some recent results concerning the evaluation of autocorrelation functions associated with 2-D autoregressive (AR) spectra are reviewed. In contrast to the 1-D case, 2-D AR autocorrelation functions can, in general, only be evaluated by means of a numerical integration. However, if the minimum-phase whitening filter for the AR process has finite reflection coefficient support, then the autocorrelation function can be evaluated algebraically, either by means of a backward 2-D Levinson algorithm, or by means of a partial fraction expansion. The special properties of 2-D AR spectra of this class make them potentially useful in the problem of finding correlation-matching spectral estimates. The possibility of performing 2-D covariance extension by fitting AR models with finite reflection coefficient Support iS partially explored.

The spectral resolution and statistical significance of a harmonic analysis obtained by low‐order maximum entropy methods (MEM) can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA‐MEM method is applied both to a synthetic time series and a time series of atmospheric angular momentum (AAM) data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, we detect reliable evidence for intraseasonal and interannual oscillations in AAM. The interannual periods include a quasi‐biennial one and a low‐frequency one, of 5 years, both related to the El Niño/Southern Oscillation. In the intraseasonal band, separate oscillations of about 48.5 and 51 days are ascertained.

주행중인 차량의 동적 거동에 대한 응답을 해석하기 위하여 시간영역에서 뿐만 아니라 주파수 영역에서의 해석이 필요하다. 주파수 영역에서의 해석을 위하여 시간영역에서의 값을 FFT를 이용하여 주파수 영역으로 변화하는 방법이 일반적으로 사용되어 왔다. 본 연구에서는 최대 엔트로피 방법을 이용하여 기존의 FFT 방법보다 차량의 과도응답특성을 시간영역 및 주파수 영역에서 편리하게 해석할 수 있는 방법을 제시하고 있다. In this paper the nonstationary response of accelerating vehicle is firstly obtained by using nonstationary road roughness model in time domain. To get the result of nonstationary response in frequency domain, the maximum entropy method is used for Processing nonstationary response of vehicle in frequency domain. The three-dimensional transient maximum entropy spectrum (MES) of response is given.

A maximum entropy approach to routing and spectral allocation in elastic optical networks is implemented using a genetic algorithm and operated on a real network topology. This approach avoids fragmentation problems and increases network utilization.

Power spectral analysis normal and pathological brainstem auditory evoked potentials

A method for finding an approximate solution of the maximum entropy (ME) method for bearing estimation is presented. It is especially suitable for the coherent source problem. This solution shows that the ME spectrum is an all-pole spectrum and the coefficients of its denominator polynomial can be found from the estimation error for the signals. Since no spatial smoothing is required, it is possible to find a solution for two closely spaced sources with a three-element array, based on single snapshot data. Depending on how the signal is estimated, it is possible to find a superresolution spectrum with the discrete Fourier transform (DFT) only.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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.

HIGH RESOLUTION 2-DIMENSIONAL POWER SPECTRAL ESTIMATION

: This tutorial paper describes the maximum entropy spectrum and the Burg technique for computing the prediction error power and prediction error filter coefficients in the associated spectral estimation formula. The maximum entropy spectrum is identical to the autoregressive spectral estimator. Also included in this paper is a discussion of the K-line spectrum, which is the wavenumber analogue of the frequency-domain maximum entropy spectrum, and the Burg technique modifications necessary for its implementation. The purpose of this paper is to provide a complete and self-contained account of the main features of the maximum entropy spectrum. Since many of the relevant mathematical derivations are not found in the formal published literature, they are incorporated in this paper. Supporting material and various sidelights of the maximum entropy spectrum appear in the appendices.

Background noise interference is one of the most important factors for low-voltage power line communication’s reliability. By analyzing the background noise of low-voltage power line communication’s channel, the background noise’s measuring circuit is set up and the AR model of the measured background noise is established. Both of them are respectively using singular value decomposition and Levinson-Durbin (LD) recursive method to calculate the AR model’s parameters and a comparative analysis of the simulation is made. The results induct: parameters acquired from the methods of singular value decomposition and LD recursive method are feasible, the parameter model from singular value decomposition is relatively complex, but extremely accurate, which is suitable for the off-line calculation and analysis of the low-voltage power line’s background noise; the parameter model from LD recursive method is very simple, but has a greater loss of accuracy, fitting for online quickly generation of the low-voltage power line’s background noise.

This paper discusses the character and differences of the solar cycle and geomagnetic cycle from the 13th to the 22nd solar cycles. The self-excitation threshold autoregressive time series model and autoregression method using maximum entropy spectrum are used to simulate and predict that the peak time of the annual average value of geomagnetic aa index is in the spring of 1994 or the Autumn of 1993. The maximum in geomagnetic annual average aa index is 26-29. The 22nd geomagnetic cycle is expected to be a middle active cycle.

This paper shows a novel hybrid approach using an Auto-Regressive (AR) model and a Quantum Recurrent Neural Network (QRNN) for classification of two classes of Electroencephalography (EEG) signals. The QRNN-AR has been shown to be capable to capture and quantify the uncertainty inherently in EEG signals because it uses fuzzy decision boundaries to partition the feature space. Two diverse element extraction techniques were used to extract the features from EEG signals; AR coefficients are processed with Levinson-Durbin algorithm and mean square error. AR provides a better frequency resolution and good spectral data of short EEG segment. The QRNN trained by the back propagation algorithm is compared with Quantum Neural Network (QNN) and Quantum Wavelet Neural Network (QWNN). The average accuracy of the proposed QRNN model is 88.28452% at 6 seconds. The Accuracy to Time Ratio (ATR) value is 14.714086, which shows the superiority of the proposed model. Experimental results demonstrate that the QRNN-AR gives the highest overall accuracy and short processing time. In addition, the structure of the proposed method is more reliable.

Source depth estimation is always a problem in underwater acoustic area, because depth estimation is a nonlinear problem. Traditional depth estimation methods use a vertical line array, which has disadvantage of poor mobility due to the size of sensor array. In order to estimate source depth with a horizontal line array, we propose a matched-mode depth estimation method based on autoregressive (AR) wavenumber estimation for a moving source in shallow water waveguides. First, we estimate the mode wavenumbers using the improved AR modal wavenumber spectrum. Second, according to the mode wavenumber estimation, we estimate the mode amplitudes by the wavenumber spectrum, which is obtained by generalized Hankel transform. Finally, we estimate source depth estimation by the peak of source depth function wherein the data mode best matches the replica mode that is calculated using a propagation model. Compared with synthetic aperture beamforming, the proposed method exhibits a better performance in source depth estimation under low signal-to-noise ratio or the small range span. The robustness of the proposed method is illustrated by simulating the performance in mismatched environment.