Description:

The course deals with the following topics - characteristics of signals, linear time invariant systems (LTI), stationary, non-stationary signals, deterministic, ergodic and stochastic processes, description of signals in continuous and discrete domains, A/D conversions and converters, sampling and quantization problems, aliasing and Nyquist's theorem, noise suppression and data preprocessing, fast and discrete Fourier transforms, efficient FFT estimation methods, other discrete transforms: z-transform, its properties and applications in DSP, inverse transforms, poles and zeros of the system, frequency response, correlation and convolution, introduction to digital filter design, FIR and IIR filters and adaptive filters, spectral analysis and spectrum estimation methods, current methods of analysis in time and frequency domain, coherence and phase characteristics, parametric and non-parametric methods, periodogram and AR spectrum.

Contents:

1. Introduction to digital signal processing (DSP). Motivation, application areas. Overview of basic operations. Convolution, correlation, digital filtering, discrete transforms. Linear time invariant systems (LTI).
2. Characteristics of random signals and their estimation. Confidence intervals, mean, standard deviation, median.
3. Stochastic processes, ergodic, stationary, non-stationary. AR, MA, ARMA data models.
4. A/D and D/A conversion. Sampling, uniform and non-uniform quantization, oversampling, anti-aliasing filtering. Nyquist theorem. Conversion errors. Signal conditioning. Aliasing. Analog filtering. Trends. Digital data formats and implications of quantization.
5. Discrete transforms, sequences and systems. Discrete Fourier Transform (DFT). Computational complexity. Gibbs effect.
6. Fast Fourier Transform (FFT). Inverse transform. Properties of the DFT. Decimation in time, decimation in frequency domain. FFT algorithm, "butterfly". Techniques for increasing the efficiency of FFT computation for real signals.
7. z-transform and its application in DSP. Features. Poles and zeros, complex plane. Frequency response. Stability of linear systems. Applications in filter design.
8. Digital filtering. Finite Impulse Response (FIR) filters. Window method. Remez exchange algorithm.
9. IIR filters (Infinite Impulse Response). Design methods. Quantization errors of coefficients. Examples of EEG signal filtering.
10. Adaptive and median filters.
11. Spectral analysis. Spectral power density. Basic methods. Parametric and non-parametric methods.
12. Periodogram and methods of its calculation. Aliasing, spectral leakage. Spectrum reciprocity, coherence and phase, chordance. Spectral analysis and signal synthesis using FFT. Absolute and relative spectrum. Disadvantages of the periodogram. Windowing.
13. Modern methods of spectrum estimation... Practical problems of spectrum estimation. Parametric models. Yule-Walker equations, LDR algorithm. Burg and Marple algorithm. Phase delay estimation.
14. Graphical representation of spectral analysis results. Topographic mapping of brain activity. Compressed spectral analysis (CSA). 3D spherical splines. Bispectrum.

Seminar contents:

1. Basic operations: unit jump and impulse response, convolution, correlation, digital filtering, discrete transform (1)
2. Basic operations: unit-jump and impulse response, convolution, correlation, digital filtering, discrete transform (2)
3. Characteristics of random signals and their estimation
4. AR, MA and ARMA data models
5. A/D and D/A conversion
6. Discrete transforms (DFT in particular)
7. z-transformation
8. Digital filtering of biosignals
9. FIR filters (Finite Impulse Response) - design and properties
10. IIR filters (Infinite Impulse Response) - design and properties
11. Design and testing of adaptive filters
12. Spectral analysis of biosignals
13. Spectrum estimation methods
14. Graphical display of spectral analysis results

Recommended literature:

Mandatory:
1. MEDDINS, Bob. Introduction to digital signal processing. Oxford: Newnes, ?2000. ix, 161 s. Essential electronics series. ISBN 0-7506-5048-6
2. IFEACHOR, Emmanuel C. a Barrie W. JERVIS. Digital signal processing: a practical approach. Harlow: Addison-Wesley, c1993. ISBN 0-201-54413-X.
3. PROAKIS, John G. a Dimitris G. MANOLAKIS. Digital signal processing. 4th ed. Harlow: Pearson Education Limited, c2014. ISBN 978-1-29202-573-5.

Recommended::
1. INGLE, Vinay K. a John G. PROAKIS. Essentials of digital signal processing using MATLAB. 3rd ed. s.l.: Cengage Learning, c2012. ISBN 978-1-111-42738-2.
2. CHAPRA, Steven C. Applied numerical methods with MATLAB: for engineers and scientists. 3rd ed. New York: McGraw - Hill, 2012. McGraw-Hill international edition. ISBN 978-007-108618-9.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar