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Analog and digital signals and noises. Frequency spectra of the signal and noise. Filtering in frequency and in time and their mutual relation. Correlation function and its application to the signal processing. Statistical methods of data processing, probability distribution, moments, correlation coefficients. Least square methods, Marquardt method. Random processes. Spectral analysis. Wavelet transform and applications. The lecture is assigned to postgraduate students and it is held in odd years, only.
Last update: T_KEVF (16.05.2005)
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The condition for completing the course is successfully passing the exam. Last update: Hrbek Tomáš, RNDr., Ph.D. (31.10.2025)
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J. Lamperti: Stochastic processes, Applied Mathematical Sciences, Springer-Verlag, New York, 1997. H. W. Ott: Noise reduction techniques in electronic systems, John Wiley and Sons, New York, 1976. H. Schmidt: Electronic analog/digital conversions, Van Nostrand Reinhold Company, New York, 1970. W. H. Press, et al.: Numerical Recipes , Cambridge University Press, Cambridge, 1992. K. Zvára, J. Štěpán: Pravděpodobnost a matematická statistika, MatfyzPress, 2001. Last update: Hrbek Tomáš, RNDr., Ph.D. (31.10.2025)
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The exam is oral, and the student is given questions based on the course syllabus within the scope presented during the lectures. Last update: Hrbek Tomáš, RNDr., Ph.D. (31.10.2025)
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1. Principles of modern measuring methods
Conversion of non-electrical to electrical quantities. Generators and detectors (detectors based on secondary emission, semiconductor detectors, coordinate sensitive detectors). Analog-to-digital conversion, quantization error and its reduction, sampling error. Methods of small signal measurement, noise reduction techniques. 2. Signal processing Time-dependent electrical signal, its frequency spectrum. Modulation (amplitude, frequency, phase), demodulation, signal mixing. Filtering of frequency spectrum and frequency conversion, their mutual relations. Classification of filtering techniques, their advantages and disadvantages. Correlation function, its approximation, synchronous detection, lock-in amplifier. 3. Statistical methods of data processing Probability, random vectors, pseudorandom sequences, bias and variance of estimates, correlation coefficients, parametric methods. 4. Data modelling Interpolation, maximum likelyhood methods, general linear least squares method, singular values decomposition (SVD): theory and examples, non-linear least squares methods, confidence intervals, Golay-Savitzky filters, splines. 5. Random processes Mean value, correlation, stationarity ergodicity, convolution, power spectra, multidimensional spectral analysis, wavelet analysis. Last update: T_KEVF (16.05.2005)
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