Signal and data processing

Lecturer:

Ondřej Klimo (gar.), Daniel Klír (gar.)

Tutor:

Ondřej Klimo (gar.), Daniel Klír (gar.)

Supervisor:

Department of Physical Electronics

Synopsis:

We aim to teach students how to apply the probability theory and mathematical statistics for processing of experimental results and to prepare them for applications of these theories in physics. Regression is explained in detail with stress laid on testing of assumptions, model and data. Discrete Fourier transform is explained and applied for deconvolution, noise elimination and signal detection. Introduction into theory of stochastic processes is preparation for following physical lectures.

Requirements:

Mathematics I,II

Syllabus of lectures:

1) Measuring errors and accuracy

2) Essentials of probability theory, characteristics of probability distributions

3) Random vector and its characteristics, probability limit theorems

4) Essentials of mathematical statistics, random sampling

5) Essentials of the estimation theory

6) Statistical hypothesis testing

7) Regression - evaluation of coefficients, error estimates, weighting, Linear and linearizable models

8) Regression - assumption, model and data testing, non-linear models, robust methods

9) Discrete Fourier transform and its applications, deconvolution

10) Noise reduction and detection of weak signal buried in noise

11) Theory of stochastic processes

12) Stationary stochastic processes, autocorrelation function of signal and of stochastic process

13) Markov chains and processes, final probabilities

Syllabus of tutorials:

1) Basic probability distributions and their characteristics

2) Hypothesis testing examples

3) Linear regression

4) Discrete Fourier transform

5) Application of convolution, correlation and autocorrelation function

Study Objective:

Knowledge:

Gain knowledge in the probability theory and mathematical statistics, regression and testing of assumptions, model and data, discrete Fourier transform and theory of stochastic processes.

Skills:

Apply the probability theory and mathematical statistics for processing of experimental results and in the theoretical physics.

Study materials:

Key references:

[1] R. J. Larsen and M. C. Marx, An Introduction to Mathematical Statistics and its Applications, Prentice-Hall , 1981.

Recommended references:

[2] J. A. Rice, Mathematical Statistics and Data Analysis, Duxbury Press , 1995.

[3] D. C. Montgomery, E. A. Peck, G. G. Viking, Introduction to Linear Regression Analysis, Textbook and Student Solutions Manual, 3rd Edition, J. Wiley

[4] N. G. van Kampen, Stochastic processes in physics and chemistry, North Holland, Amsterdam 1992

W.H. Press, B.P. Flannery, S.A. Teukolsky, V. H. Vetterling,

[5] Numerical Recipes in Pascal (The art of scientific computation), Cambridge University Press, Cambridge 1989. (also versions for C and Fortran)

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: