- Department of Mathematics
The course is devoted to modern techniques of the analog and digital signal processing used in physics, measurements and information science. Basic signal transforms and their discrete equivalents are explained to describe signals and their transfer in different representations. Practical training is based on MATLAB software with Signal and Wavelet Toolboxes.
Basic course of mathematical analysis, functional analysis, complex variable functions, differential equations, Fourier series and transform, basics of MATLAB programming (in the extent of the courses 01MA1, 01MAA2-4, 01LA1, 01DIFR, 01MMF, 01NAH, 01FKP held at the FNSPE CTU in Prague).
- Syllabus of lectures:
1. Backgrounds of programming in MATLAB with Signal Toolbox. 2. Systems and signals continuos and discrete in time. Time and amplitude discretization. Sampling theorem. 3. Deterministic and stochastic signals. Linear time invariant systems. 4. Description and properties of systems. Harmonic signals, Haeviside and delta function. 5. Discrete signals description in time and frequency domain. Convolution, Laplace and Fourier transform, Fourier series and spectral analysis. 6. Hilbert transform, analytical signals, Z-transform. 7. Transfer function and impulse response of the system. 8. Signals generation and their spectral analysis in MATLAB. 9. Digital signal filters with finite and infinite response. 10. Digital filter design in MATLAB. 12. Time-frequency signal representation. Window Fourier transform. 13. Wavelet transform and the MATLAB Wavelet Toolbox.
- Syllabus of tutorials:
Practical computer training and demonstrations of the Digital Signal Processing are integral part of the course and they are performed on the MATLAB platform with the use of Signal and Wavelet toolboxes.
- Study Objective:
Basic knowledge on mathematical treatment of linear systems and signals. Practical importance of various signal representations and processing. Integral transforms and their discrete counterparts, signal sampling and filtering, spectral analysis of data. Skills: Digital Signal Processing in MATLAB, design of digital filters and transfer systems. Interpretation of spectral and wavelet analysis.
- Study materials:
 Davídek V., Sovka P.: Číslicové zpracování signálů a implementace. (Skriptum FEL ČVUT, Vydavatelství ČVUT, Praha, 1999),
 Sedláček M.: Zpracování signálů v měřící technice. (Skriptum FEL ČVUT, Vydavatelství ČVUT, Praha, 1993),
 Sovka P., Pollák P.: Vybrané metody číslicového zpracování signálu. (Skriptum FEL ČVUT, Vydavatelství ČVUT, Praha, 2001),
 Krauss P.T., Shure L., Little J.N.: Signal Processing Toolbox for MATLAB. (The MATHWORKS Inc., Natick, Mass., 1993-2005; www.mathworks.com ),
 Vích R., Smékal Z. : Číslicové filtry. (ACADEMIA, Praha, 2000)
 Oppenheim A.V., Schaffer R.W.: Discrete Time Signal Processing. (Prentice-Hall, Englewood Cliffs, New Jersey,1990),
 Mertins A.: Signal Analysis - Wavelets, Filter Banks, Time-Freq. Transforms. (John Wiley & Sons, Chichester, N.Y.,1999),
 Porat B.: A Course in Digital Signal Processing. (MATLAB based books, J.Wiley and Sons, Inc., 1997; www.mathworks.com/support/books/),
 Poularikas A.D.: The Handbook of Formulas and Tables for Signal Processing. (CRC Press LLC, IEEE Press, Huntsville, 1999),
 Mallat S.: A Wavelet tour of signal processing. (Academic Press, San Diego, 1999),
 Smith S.W.: The Scientist and Engineer's Guide to Digital Signal Processing. (2nd Edition, California Technical Publishing, San Diego 1999; www.DSPguide.com)
Media and tools: Computer training room with
programming language MATLAB complemented with SIGNAL and WAVELET Toolbox. .
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans: