Statistical analysis and digital processing of the Mössbauer spectra

This work is focused on using the statistical methods and development of the filtration procedures for signal processing in Mossbauer spectroscopy. Statistical tools for noise filtering in the measured spectra are used in many scientific areas. The use of a pure statistical approach in accumulated Mossbauer spectra filtration is described. In Mossbauer spectroscopy, the noise can be considered as a Poisson statistical process with a Gaussian distribution for high numbers of observations. This noise is a superposition of the non-resonant photons counting with electronic noise (from γ-ray detection and discrimination units), and the velocity system quality that can be characterized by the velocity nonlinearities. The possibility of a noise-reducing process using a new design of statistical filter procedure is described. This mathematical procedure improves the signal-to-noise ratio and thus makes it easier to determine the hyperfine parameters of the given Mossbauer spectra. The filter procedure is based on a periodogram method that makes it possible to assign the statistically important components in the spectral domain. The significance level for these components is then feedback-controlled using the correlation coefficient test results. The estimation of the theoretical correlation coefficient level which corresponds to the spectrum resolution is performed. Correlation coefficient test is based on comparison of the theoretical and the experimental correlation coefficients given by the Spearman method. The correctness of this solution was analyzed by a series of statistical tests and confirmed by many spectra measured with increasing statistical quality for a given sample (absorber). The effect of this filter procedure depends on the signal-to-noise ratio and the applicability of this method has binding conditions.

[1]  James D. Hamilton.  Time Series Analysis , 1994 .

[2]  J. Royston.  The W Test for Normality , 1982 .

[3]  G. W. Snedecor.  Statistical Methods , 1964 .

[4]  J. Pechoušek,et al.  Digital proportional-integral-derivative velocity controller of a Mössbauer spectrometer , 2008 .

[5]  Petre Stoica,et al.  Introduction to spectral analysis , 1997 .

[6]  G. Marsaglia,et al.  Evaluating Kolmogorov's distribution , 2003 .

[7]  Z. Birnbaum,et al.  One-Sided Confidence Contours for Probability Distribution Functions , 1951 .

[8]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[9]  J. P. Royston,et al.  Algorithm AS 181: The W Test for Normality , 1982 .

[10]  Z. Klencsár,et al.  User-friendly software for Mössbauer spectrum analysis , 1996 .

[11]  J. Royston.  An Extension of Shapiro and Wilk's W Test for Normality to Large Samples , 1982 .

[12]  P. Royston.  A Remark on Algorithm as 181: The W‐Test for Normality , 1995 .

[13]  K. R. Reddy,et al.  Dual modulation phase-lock technique for Mössbauer resonance spectroscopy , 1981 .

[14]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[15]  D. L. Nagy,et al.  An overview on model-independent data reduction methods in Mössbauer spectroscopy , 1991 .

[16]  P. Welch.  The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[17]  J. Durbin.  Distribution theory for tests based on the sample distribution function , 1973 .

[18]  K. R. Reddy,et al.  Correlation techniques for the improvement of signal-to-noise ratio in measurements with stochastic processes , 2003 .