Algorithms for least‐squares linear prediction and maximum entropy spectral analysis—Part II: Fortran program

Geophysics ◽  
1980 ◽  
Vol 45 (3) ◽  
pp. 433-446 ◽  
Author(s):  
I. Barrodale ◽  
R. E. Erickson
Keyword(s):  
Spectral Analysis ◽  
Least Squares ◽  
Maximum Entropy ◽  
Linear Prediction ◽  
Fortran Program ◽  
Prediction Problem ◽  
Maximum Entropy Spectral Analysis ◽  
Least Squares Algorithm ◽  
Toeplitz Structure

We present a set of Fortran subroutines which implement the least‐squares algorithm described in Part I (Barrodale and Erickson, 1980, this issue) for solving three variants of the linear prediction problem. When combined with a suitable driver program, these subroutines can be used to calculate maximum entropy spectra without imposing a Toeplitz structure on the model.

Algorithms for least‐squares linear prediction and maximum entropy spectral analysis—Part I: Theory

Geophysics ◽  
1980 ◽  
Vol 45 (3) ◽  
pp. 420-432 ◽  
Author(s):  
I. Barrodale ◽  
R. E. Erickson
Keyword(s):  
Spectral Analysis ◽  
Least Squares ◽  
Maximum Entropy ◽  
Linear Prediction ◽  
Fortran Program ◽  
Computationally Efficient ◽  
Rounding Errors ◽  
Maximum Entropy Spectral Analysis ◽  
Short Sample ◽  
Toeplitz Structure

Experience with the maximum entropy spectral analysis (MESA) method suggests that (1) it can produce inaccurate frequency estimates of short sample sinusoidal data, and (2) it sometimes produces calculated values for the filter coefficients that are unduly contaminated by rounding errors. Consequently, in this report we develop an algorithm for solving the underlying least‐squares linear prediction (LSLP) problem directly, without forcing a Toeplitz structure on the model. This approach leads to more accurate frequency determination for short sample harmonic processes, and our algorithm is computationally efficient and numerically stable. The algorithm can also be applied to two other versions of the linear prediction problem. A Fortran program is given in Part II.

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.

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