Digital Signal Processing

Lecturer:

Vladimír Krajča (gar.)

Tutor:

Vladimír Krajča (gar.)

Supervisor:

Department of Biomedical Technology

Synopsis:

The topic of the subject is to improve understanding of the basic notions, formulas and methods of digital signal processing. The theory is illustrated by application to both real and simulated signals. Except of description of signal characteristics and numerical parameter computing, the methods and tools of data visualization are discussed.Special attention is paid to digital signal filtering and modern spectrum analysis methods.

Requirements:

Syllabus of lectures:

1.Introduction to digital signal processing (DSP). Motivation, areas of application. Biosignals processing

2.Random signals characteristics and parameters estimation. Data models.

3.Stochastic processes, ergodic, stationary, nonstationary. Confidence intervals, mean, variance, standard deviation, histogram, median

4.Basic DSP operations: Unit impulse and unit step response. Convolution, correlation , filtering, discrete transformations. Linear time-invariant systems (LTI).

5.Signal digitization. Sampling and quantization. Nyquist theorem. Aliasing and anti-aliasing filtering, oversampling.

6.Discrete transforms, sequences and systems. Discrete Fourier transform (DFT). Properties of DFT. Computing complexity. Gibbs phenomenon. Fast Fourier Transform (FFT). Decimation in time, decimation in frequency. Efficient techniques for real signals. Inverse Fourier transform.

7.z-transform and its application in DSP. Properties. Poles and zeros, complex plane. Frequency response. Stability. Filters design.

8.Digital filtering. FIR filters (Finite Impulse Response). Window method..

9.IIR filters (Infinite Impulse Response). Filters design. Examples of EEG signal filtering.

10.Median filters, properties, applications. Adaptive filtering. Basic types and properties.

11.Spectrum analysis, basic methods, parametric and nonparametric methods of spectrum estimation. Spectral power density. Periodogram. Spectral analysis and synthesis using FFT.

12.Cross spectrum, coherence, phase. Absolute, relative, logarithmic spectrum. Windowing. Spectral leakage. Phase delay estimation.

13.Modern methods of spectrum estimation. Practical problems. Parametric models. Yule-Walker equations, LDR algorithms. Burg algorithm.

14.Graphic visualization of spectrum analysis results. Topographic mapping of electrical activity of brain. Compressed spectral arrays(CSA). 3D spherical splines. Bispectrum.

Syllabus of tutorials:

1.MATLAB Tutorial

2.Basic DSP operations

3.Random signals charactereistics

4.Principles of A/D and D/A conversion

5.Discrete transforms (DFT)

6.z-transform

7.Digital filtering

8.IIR filters (Infinite Impulse Response)

9.FIR filters (Finite Impulse Response)

10.Spectrum analysis

11.Modern methods of spectrum estimation

12.Numerical parameters graphic visualization

13.Nonstationary signals processing (Wavelet transform, STFT - Short-Time Fourier Transform)

14.Automatic classification for signal processing

Study Objective:

Study materials:

[1]Uhlíř J., Sovka P., Číslicové zpracování signálů, ČVUT FEL, 1995 (povinná)

[2]Ifeachor E. C., Jervis B.W. Digital Signal Processing. A Practical Approach. Second Edition, Prentice Hall 2002.

[3]Lyons R.G., Understanding Digital Signal Processing.. Prentice Hall 2001. (doporučená)

[4]Smith S.W. Digital Signal Processing. A Practical guide for Engineers and Scientists. Newness, Elsevier. 2003.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Navazující magisterský studijní obor Biomedicínský inženýr - prezenční (compulsory course)