Students will deepen their knowledge in mathematics and statistics and apply it on real problems of signal processing. During the course, they will get acquainted with math- and visualization-SW Matlab.

1. Introduction, motivation, organization of the course. Examples of signal processing systems. Basic classification of signals - continuous/discrete time, periodic/non-periodic. Transformation of time.
2. Continuous and discrete time periodic signals: sinusoids and complex exponentials. Overview of basic notions in complex numbers. Discrete and continuous time systems. Linear, time invariant systms (LTI). Representation of signals as series of pulses, convolution. Describing systems using differential and difference equations.
3. Continuous time signals and their frequency analysis: periodic - Fourier series, coefficients. Non-periodic - Fourier transform, spectral function. Spectra of typical signals. Signal energy - Parseval's theorem.
4. Continuous-time systems - Laplace transform, transfer function, frequency response, stability. Example of a simple analog circuit.
5. Sampling and reconstruction - ideal sampling, aliasing, sampling theorem. Spectrum of sampled signal, ideal reconstruction. Normalized time and frequency. Quantization.
6. Discrete-time signals and their frequency analysis - Discrete Fourier series, Discrete-time Fourier transform. Circular convolution, fast convolution.
7. Discrete Fourier transform (DFT) and what it really computes. Fast Fourier transform.
8. Discrete systems - z-transform, finite and infinite impulse response systems (FIR and IIR), transfer function, frequency response, stability. Example of a digital filter: MATLAB and C.
9. Discrete systems cont'd: design of simple digital filters, sampling of frequency response, windowing. Links between continuous-time and discrete-time systems.
10. Two-dimensional (2D) signals and systems: space frequency, spectral analysis (2D-Fourier transform), filtering using a mask. Example - JPEG.
11. Random signals - random variable, realization, distribution function, probability density function (PDF). Stationarity and ergodicity. Parameters of a random signal: mean, etc. Estimation - ensemble and temporal.
12. Random signals cont'd: correlation function, power spectral density (PSD). Processing of random signals by LTI systems.
13. Summary of basic notions, systematic organization of signal processing knowledge. Examples.

• participation in computer labs is not checked but active participation and presentation of results to the tutor is evaluated by 2 pts.
• Groups in computer labs are organized according to inscription into schedule frames.

• recommended prerequisite
  • Mathematical Analysis 1
  • Discrete Mathematics
  • Mathematical Analysis 2

• Oppenheim A.V., Wilski A.S.: Signals and systems, Prentice Hall, 1997

• http://www.fit.vutbr.cz/study/courses/ISS/public/
• Jan, J., Kozumplík, J.: Systémy, procesy a signály. Skriptum VUT v Brně, VUTIUM, 2000.
• Šebesta V.: Systémy, procesy a signály I., Skriptum VUT v Brně, VUTIUM, 1997.
• Jan J., Číslicová filtrace, analýza a restaurace signálů, VUT v Brně, VUTIUM, 2002, ISBN 80-214-1558-4.

• Programme IT-BC-3 Bachelor's

  branch BIT , 2. year of study, winter semester, compulsory