Maximum Entropy Spectral Analysis Method Research Articles

Analysis of broadening mechanism of ionospheric echo spectrum and spectrum sharpening method

High-frequency sky wave detection equipment must rely on the ionosphere as the propagation medium in the early warning and sea state remote sensing tasks. The ionosphere is time-varying and unstable, which will change the characteristics of the high-frequency electromagnetic wave propagating through it, resulting in the broadening of the echo spectrum, thus seriously affecting the detection of targets and the inversion of sea state parameters. The reason and mechanism of the echo spectrum expansion are analyzed in detail from the dispersion effect, phase contamination and multimode propagation. The bandwidth of the dispersion effect is different from that of the high frequency detection equipment. When the bandwidth of the sky wave equipment is 3–30 MHz, the bandwidths of the dispersion effect are 41.6–57.4 kHz and 0.17–10.8 MHz. The multi-quasi-parabolic ionospheric model is used to discuss the frequency selection measures to avoid multimode propagation. The modulation process of ionospheric contamination to echo is studied theoretically. It is shown that the non-linear phase contamination will cause the energy of echo to diffuse in frequency domain and to be unable to accumulate. To solve the problem of phase contamination which is difficult to solve in practice, a contamination correction method without estimating the instantaneous frequency of the echo is proposed. In the method the consistency principle of signal subspace and signal frequency vector expansion space is used, and therefore the phase contamination term can be well estimated. Based on the real data, the contamination correction results from the proposed method, phase gradient autofocus method, maximum entropy spectral analysis method and time-frequency processing method are given. The results show that the new method is a better method and can effectively sharpen the broadened echo spectrum.

Period identification in hydrologic time series using empirical mode decomposition and maximum entropy spectral analysis

Identification of periods is a key issue in hydrologic time series analysis. It is also a difficult task in practice when analyzing hydrologic series with complicated stochastic characteristics. In this paper, a new method of period identification is proposed in which empirical mode decomposition (EMD) and maximum entropy spectral analysis (MESA) are used in combination. The EMD method is capable of adaptively decomposing a series into a set of components called intrinsic mode functions (IMFs). By comparing the IMEs with the spread function of white noise with proper confidence level, different components of original series can be identified. These components may correspond to noise or true IMEs under different temporal scales. The EMD method can distinguish the type. The actual periods of original hydrologic series can be identified by analyzing each of the true IMEs using MESA. Analyses of both synthetic and observed series data indicated better performance of the proposed EMD-MESA method to identify periods. Compared with the conventional MESA method which is widely used presently, the EMD-MESA method can effectively avoid the influence of noise and trend on period identification, and it can accurately identify periods even in the case of series with multiple-peaked spectra. Therefore. EMD-MESA not only can improve the period identifying capability of MESA, but also can improve overall period identification by being able to distinguish noise, period, and trend. (C) 2012 Elsevier B.V. All rights reserved.

Preoperative Ultra Short-Term Entropy Predicts Arterial Blood Pressure Fluctuation During the Induction of Anesthesia

In this study, we sought to determine whether the preoperative nonlinear index of heart rate variability, ultra short-term entropy (UsEn), could predict cardiovascular responses to the induction of general anesthesia. UsEn was estimated by a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method (MemCalc method). Preoperative UsEn of 46 patients (ASA PS 1 or 2, aged 40-60 yr) without a history of hypertension was evaluated using the MemCalc method. Patients were assigned to two groups according to preoperative UsEn (Group LOW; UsEn <45, Group HIGH; UsEn > or =45). Anesthesia was induced with propofol, fentanyl and vecuronium bromide and endotracheal intubation was performed. Hemodynamic fluctuations during the induction of anesthesia were recorded and compared between the two groups. It was found that arterial blood pressure fluctuations during the induction of anesthesia were significantly greater in patients with a low UsEn. UsEn could predict arterial blood pressure fluctuations during the induction of anesthesia.

A maximum entropy analysis of global monthly series of rainfall from merged satellite data

This Letter presents the results of analysing a global, satellite‐based monthly precipitation database on a 2.5° latitude‐longitude grid for the 22‐year period from 1979 to 2001 using a direct maximum entropy spectral analysis method. The NOAA Climate Prediction Center (CPC) Merged Analysis of Precipitation (CMAP) database is used to calculate the rainfall cycles for ∼10 000 time series covering the whole Earth. It is shown that several cycles other than the annual or seasonal cycles affect the rainfall distribution of many areas, in particular western Europe.

Prediction Analysis for Measles Epidemics

A newly devised procedure of prediction analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed. This method was applied to time series data of measles case notification in several communities in the UK, USA and Denmark. The dominant spectral lines observed in each power spectral density (PSD) can be safely assigned as fundamental periods. The optimum least squares fitting (LSF) curve calculated using these fundamental periods can essentially reproduce the underlying variation of the measles data. An extension of the LSF curve can be used to predict measles case notification quantitatively. Some discussions including a predictability of chaotic time series are presented.

EFFECT OF RAPID INHALATION INDUCTION IN CHILDREN ON HEART RATE VARIABILITY ASSESSED BY NEW MAXIMUM ENTROPY SPECTRAL ANALYSIS METHOD

S422 The new method of time series analysis (MemCalc), which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was introduced [1]. This method can be used for segments of small data length and determine the rapidly varying short term fluctuation. This study examined spectral components of heart rate variability (HRV) by MemCalc as an indicator of the autonomic hemodynamic control during rapid induction of 3% halothane and 5% sevoflurane anesthesia. METHODS: After institutional approval and informed consent, unpremeditated 32 pediatric patients (ASA PS I) undergoing eye surgery were studied. Group 1 (n=16, age;6.5 +/- 2.5yr) received 3% halothane in 100% oxygen. Group 2 (n=16, age; 6.5 +/- 1.9yr,) received 5% sevoflurane in 100% oxygen. All patients were allowed to breath spontaneously through mask for 10 min, and then ventilated manually for 5 min. RR intervals of ECG were measured before induction of anesthesia and thereafter throughout the period of the study. Successive spectral analysis of RR intervals time series was performed on every one-min segment of data by MemCalc. The areas of the spectral peaks within each measurement were calculated as follows: low-(LF, 0.04-0.15 Hz) and high-frequency area(HF, 0.2-0.7 Hz). The responses of time-dependent fluctuation of LF, HF and LF/HF ratio were evaluated by a repeated measured ANOVA. RESULTS: Results are shown in Table 1.Table 1: Changes in LF and HFDISCUSSION: LF, HF and LF/HF ratio of RR intervals obtained by MemCalc method revealed different time-dependent changes of autonomic hemodynamic control during rapid induction of anesthesia with 3% halothane and 5% sevoflurane.

Oscillatory growth movements of roots in weightlessness

The gravitropic curvature of lentil roots (Lens culinaris L. cv. Verte du Puy), grown in near weightlessness and stimulated on a 1‐g centrifuge for 5 to 60 min was followed by time lapse photography. The experiment was carried out in the frame of the IML 1 Mission of Spacelab. Due to the applied acceleration field, the tip of the roots bent and reoriented with respect to the acceleration vector. However, visual inspection of the data could indicate an oscillatory movement superimposed on the gravitropic reorientation.We applied two signal processing techniques, fast Fourier transform (FFT) and maximum entropy spectral analysis (MESA), to provide quantitative data about the oscillatory movements of the lentil roots under gravity free conditions. In the case with very few data points in the time series the MESA method is superior to the conventional FFT. In the lentil root movements, the Fourier analysis could not extract and resolve the oscillatory signals present in the time series. The MESA approach revealed oscillations with periods around 35 and 50 min for the present lentil roots.Circumnutations are, therefore, present in roots also in weightlessness.

New Method of Time Series Analysis and Its Application to Wolf's Sunspot Number Data

A newly devised procedure of time series analysis, which is a linearized version of the nonlinear least squares method combined with the maximum entropy spectral analysis method, was proposed and applied to the annual sunspot number data from 1700 to 1991. Multiple periodicities of the temporal variation were elucidated in detail. The solar cycle of a 11.04-year period accompanied with the solar cycle multiplets, the periods of 50.41 years, the so-called “Yoshimura cycle”, and 107.11 years corresponding to the cycle of century-scale minima, for example, were clearly observed. The optimum least squares fitting curve for the data was extended over the past two millennia and the next millennium. The past grand minima such as the Maunder minimum were confirmed in the past extrapolation curve, and the next centennial minimum was predicted to occur between 2000 and 2030.

Maximum entropy spectral analysis of volcanic tremor using data from Etna (Sicily) and Merapi (central Java)

The maximum entropy spectral analysis (MESA) method is applied to synthetic and observed tremor time series using autoregressive processes and recordings from the volcanoes Etna (Sicily) and Merapi (central Java). The MESA analysis can be used to estimate power spectra with sharp peaks from short data records. If the tremor source process can be modelled by an autoregressive process, the MESA method is well-suited for determining the coefficients of the underlying difference equations. As in the standard periodogram method of power spectrum estimation, a mesagram estimate using record segmentation and MESA spectrum averaging reduces the variance of the spectral estimator. In combination with periodogram estimates, mesagram estimates confirm that the tremor source may be modelled as an ensemble of randomly excited resonators. Used together, these estimates provide a valuable method for short-term monitoring of volcanic activity. In addition, they can be applied to the determination of new source parameters such as resonator frequencies, damping coefficients, excitation probabilities, correlation of exciting forces, and resonator coupling and in the pattern recognition of source types.

A High-Resolution Spectral Study of Audiomagnetotelluric Data and Noise Interactions

This study is an investigation of the behaviour of audiomagnetotelluric (AMT) response estimates, in the presence of intense anthropogenic noise. The details of the data and noise interactions are studied by constructing highly resolved AMT response functions using the Maximum Entropy spectral analysis method, in its multichannel form. For low-noise, consistent data spectral estimates and their frequency resolution should be independent of the spectral technique used. Such behaviour is confirmed. When the data are contaminated by significant amounts of noise the highly-resolved estimates display detailed inconsistencies as a function of frequency. Such piecewise distortions can be understood if the response function is viewed as a polynomial. The results obtained enable the identification of response structure generated by both harmonic and subharmonic noise processes. High-resolution estimates provide a detailed view of data quality and narrow-band perturbations. The comparison of high-resolution response functions with conventional (discrete) estimates, shows that, in some cases, the latter may produce erroneous estimates. A discussion of the generation and received characteristics of noise waveforms is also included. A smoothing operation, involving frequency domain convolution, is described and applied to the results obtained. The technique exploits the minimum-delay properties exhibited by a valid impulse response function in the time domain.

Maximum entropy spectral analysis of hydrologic data

Determination of periodicities is a frequently encountered problem in stochastic analysis of hydrologic time series data. Conventional methods of spectral analysis such as those currently used in the analysis of hydrologic data have some long recognized disadvantages. The maximum entropy spectral analysis (MESA) method was developed as an alternative to conventional spectral analysis and has received considerable attention in exploratory geophysics. Several aspects of application of MESA to hydrologic time series are discussed in this paper. The performance of the MESA method is compared with the commonly used Blackman and Tukey method. MESA can be extended to obtain additional stochastic characteristics such as autocorrelation, partial autocorrelation, inverse autocorrelation, inverse partial autocorrelation, and cross spectra of time series data. Thus spectral analysis and computations related to stochastic model development may be integrated by using MESA. The simple relationship between maximum entropy and maximum likelihood spectra may be used to filter our pseudoperiodicities that occur in maximum entropy spectra estimated by using large filter orders.

A Comparison of Traditional Fourier and Maximum Entropy Spectral Methods for Vibration Analysis

The structural vibrations monitored on a process plant often contain burst phenomena where several discrete frequencies are present. Spectral analysis of these vibration signals by Fourier transform methods is generally considered incapable of resolving discrete frequencies close together in a short time slice. The power spectral density estimates computed by traditional Fourier transform methods are compared with those computed by more recent maximum entropy spectral analysis (MESA) methods for both data from a test system where the outputs of two tuned filters, excited by pseudo-random binary noise, are summed, and the vibration signals from an accelerometer mounted on a die in an extrusion process. The frequency resolution characteristics of the two methods are compared, and the problems associated with the choice of an optimum order autoregressive prediction error filter for the MESA method are discussed.

Covariance Characterization by Partial Autocorrelation Matrices

It is known that the autocorrelation function of a stationary discrete-time scalar process can be uniquely characterized by the so-called partial autocorrelation function, which is a sequence of numbers less or equal to one in magnitude. We show here that the matrix covariance function of a multivariate stationary process can be characterized by a sequence of matrix partial correlations, having singular values less than or equal to one in magnitude. This characterization can be used to extend to the multivariate case the so-called maximum entropy spectral analysis method.