ON POWER ESTIMATION IN MAXIMUM ENTROPY SPECTRAL ANALYSIS

Geophysics ◽  
1978 ◽  
Vol 43 (4) ◽  
pp. 681-690 ◽  
Author(s):  
S. J. Johnsen ◽  
N. Andersen
Keyword(s):  
Spectral Analysis ◽  
Spectral Density ◽  
Maximum Entropy ◽  
Power Estimation ◽  
Low Noise ◽  
Density Estimator ◽  
Simple Method ◽  
Power Estimate ◽  
Maximum Entropy Spectral Analysis ◽  
Harmonic Components

A conceptually simple method for power estimation in maximum entropy spectral analysis, based on evaluation of complex residues of the spectral density estimator, is suggested. Numerical integration of the peaks of the power density function is thus avoided. The agreement in simple cases with conventional estimates is demonstrated, and the explicit performance is analyzed in detail in a series of examples. The close connection between the residue power estimate and the estimate proposed recently by Pisarenko is pointed out. The method is particularly suitable for spectral decomposition of low noise time series with several harmonic components, because it allows a direct listing of frequency and power estimates, provides an indication of the purity of the obtained harmonic components and enhances the resolution of the maximum entropy spectral density estimator. Computing facilities with modern program libraries are required for efficient use of the method.

Comparison of maximum entropy spectral analysis (MESA) and least‐squares linear prediction (LSLP) methods for some artificial samples

Geophysics ◽  
1982 ◽  
Vol 47 (12) ◽  
pp. 1731-1736 ◽  
Author(s):  
R. P. Kane ◽  
N. B. Trivedi
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Prediction Error ◽  
Linear Prediction ◽  
Low Noise ◽  
Good Resolution ◽  
Maximum Entropy Spectral Analysis ◽  
Final Prediction Error ◽  
Wide Range ◽  
Data Length

Spectral analysis is a very useful technique for studying geophysical problems. In earlier days, the only methods available were those of Fourier analysis or the method of Blackman and Tukey (1959) based on autocorrelation function. Recently, Burg (1967, 1968) introduced maximum entropy spectral analysis (MESA) which gives good resolution even for periods comparable to the data length. Ulrych and Bishop (1975) gave a critical appraisal of Burg’s algorithm. Several workers noticed and reported some inherent shortcomings. Thus, Chen and Stegan (1974) showed that, for truncated sinusoids, the spectral maxima showed frequency shifts sometimes as large as 20 percent, depending upon the initial phase and the length of the sample. Also, under certain conditions, the Burg spectra display line‐splitting in the presence of low noise, and as the noise is increased, the multiple peaks coalesce into a single peak shifted substantially away from the correct value (Fougere et al, 1976; Fougere, 1977). These defects can be rectified by the elaborate computer program given by Fougere (1977). Another difficulty is in selection of the appropriate length of the prediction error filter (LPEF). Whereas low LPEF is generally inadequate to resolve all the peaks, high LPEF, while resolving all peaks, produces instability in the spectra and gives spurious peaks. For determining the optimum LPEF, Ulrych and Bishop (1975) suggested the use of the Akaike’s (1969) final prediction error (FPE) criterion. And if this failed, an LPEF of about 50 percent of the data length was suggested to be generally adequate. Gutowski et al (1978) suggested the use of partial correlation coefficient. Berryman (1978) suggested an empirical solution [Formula: see text] where N = number of data points. Our experience (Kane 1977, 1979) indicated that for samples containing peaks in a wide range of frequency LPEF of about 50 percent of data length was adequate to resolve frequencies exceeding the fifth harmonic, while for lower harmonics, LPEF even as high as 90 percent was sometimes needed, with the danger of peak‐splitting ever present.

Transient Rhythms in the Swimming Activity of Sarsia Tubulosa (Hydrozoa)

1982 ◽  
Vol 96 (1) ◽  
pp. 181-193
Author(s):  
JANET L. LEONARD
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Swimming Activity ◽  
Endogenous Rhythms ◽  
Maximum Entropy Spectral Analysis ◽  
Transient Nature ◽  
High Degree ◽  
Behavioural Mechanism

Maximum entropy spectral analysis (MESA) was used to assess the contribution of endogenous rhythms to the timing of swim bouts in a hydrozoan jellyfish, Sarsia tubulosa M. Sars. The results show that the high degree of variability in Sarsia swimming activity is due largely to the number of rhythms which may contribute to the behaviour and to the transient nature of these rhythms. I conclude that the ability to ‘choose’ among behavioural rhythms may be a widespread behavioural mechanism in cnidarians and I suggest that, in Sarsia, these transient behavioural rhythms may originate in activity of the marginal pacemaker system.

Maximum entropy spectral analysis of the Duero Basin

1995 ◽  
Vol 15 (4) ◽  
pp. 463-472 ◽  
Author(s):  
Solange Mendonça Leite ◽  
José Pinto Peixoto
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Maximum Entropy Spectral Analysis ◽  
Duero Basin

Application of maximum entropy spectral analysis to estimation of parameters of ARMA models by the ITIF method

1985 ◽  
Vol 21 (14) ◽  
pp. 611 ◽  
Author(s):  
R. Gómez Martín ◽  
M.C. Carrión Perez ◽  
S. Al Khouri Ibrahim ◽  
B. García Olmedo
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Arma Models ◽  
Estimation Of Parameters ◽  
Maximum Entropy Spectral Analysis

To: “Maximum Entropy Spectral Analysis of Multiple Sinusoids in Noise”, by E. H. Satorius and J. R. Zeidler, in GEOPHYSICS, v. 43, no. 6, p. 1111–1118 (October 1978).

Geophysics ◽  
1979 ◽  
Vol 44 (2) ◽  
pp. 277-277
Keyword(s):  
Spectral Analysis ◽  
Maximum Entropy ◽  
Maximum Entropy Spectral Analysis

The figure captions for Figures 1 and 2 should be interchanged in the paper, “Maximum Entropy Spectral Analysis of Multiple Sinusoids in Noise”, by E. H. Satorius and J. R. Zeidler, in Geophysics, v. 43, no. 6, p. 1111–1118 (October 1978).

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