Course detail

Digital Signal Processing

FEKT-CCZSAcad. year: 2015/2016

One-dimensional and two-dimensional discrete signals and systems. Description of systems, differential equations. Z- transform, solving of systems, transfer function, impulse response properties of the system. . Discrete Fourier transform, FFT. Basic of design FIR and IIR digital filters. Complex and real cepstrums. Application of cepstrums to speech and image processing. Signal quantization in discrete systems. Realization of digital filters and FFT in digital signal processors.

Language of instruction

English

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Mišurec, CSc.

Department

Department of Telecommunications (UTKO)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

The student of the subject Digital signal processing will understand basic algorithms for digital signal processing and he will be able to independently apply and model the basic functions of digital processing in Matlab. It will have a basic idea of the implementation of the algorithms on microprocessors and digital signal processors. Students will primarily term:
- Discrete signals and their description
- Discrete systems and their description
- Status of description systems
- Z -Transformation and its application in solving digital systems
- Frequency analysis of discrete signals
- Discrete system - frequency selective filter
- Discrete Fourier transformation
- Technical means of digital signal processing

Prerequisites

Students should have basic knowledge of mathematics and physical description of the signal, which gets in the mandatory subjects in the previous study. Their graduating is not a prerequisite for registration of this subject.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Techning methods include lectures, computer laboratories and practical laboratories. Course is taking advantage of e-learning (Moodle) system

Assesment methods and criteria linked to learning outcomes

0-20 points - written test in exercises (optional part).
0-10 points - test using computers and software, (optional part).
0-70 points - written exam, compulsory part of the completion of the course.
Exam is focused to verify the orientation of the basic problems of digital processing, their description, calculation methods, the characterization of systems analysis and synthesis of digital systems.

Course curriculum

1. Discrete signals - basic discrete signals, classification of one dimensional discrete signals.
2. Discrete signals - multi dimensional discrete signals, correlation of discrete signals.
3. Discrete systems - initial conditions, discrete systems as block diagrams.
4. Discrete systems - classification of discrete systems, linear time invariant system, combination of discrete time invariant systems, causallity and stability of time invariant systems, FIR and IIR systems.
5. State diagram of linear time invariant system.
6. Z- transform and using.
7. Frequency analysis of discrete signals - time discrete Fourier line, spectral power, FT of discrete aperiodic signal, feature of FT, cepstrum.
8. Frequency characteristics of linear time invariant system, frequency filters, lowpass filter, highpass filter, digital resonator, bandpass filter, notch filter, comb filter, phase filter.
9. Discrete FT definition, features, vector form of DFT, relationship between DFT and Z - transform.
10. Inverse systems and deconvolution - reciprocal disrete systém, geometric interpretation of the frequency response, linear time-invariant discrete system with minimum, maximum and mixed-phase homomorphic deconvolution.

Work placements

Not applicable.

Aims

The aim of the course is to provide students with a coherent explanation of the basic theory of digital signal processing with an emphasis on understanding the computational algorithms used in digital processing. Especially emphasized are methods for describing digital systems, especially digital filters. The subject is closed by discussions about the implementation of DSP algorithms in microprocessors and digital signal processors.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

MITRA,S.K., Digital Signal Processing-A Computer-Based Approach. The McGraw-Hill Companies, Inc. New York 1998
OPPENHEIM, A.L., SCHAFER, R.W., Digital Signal Processing, Prentice-Hall, Inc. New Jersey, 1995.
VÍCH.R., Z Transform Theory and Applications. D.REidel Publishing Company, Dordrecht 1987.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EECC Bc. Bachelor's

    branch BC-MET , 2 year of study, summer semester, elective specialised

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

prof. Ing. Jiří Mišurec, CSc.

Syllabus

Discrete signals and systems. Discrete signals - sequences. Linear time-invariant discrete system. Stability and causality. Frequency representation. Sampling of continuous signals, aliasing. Two-dimensional signals and systems.
Z-transform, convergence region and properties. Inverse z-transform and its calculation by means of the residue theorem. Solution of difference eqations using the z-transform.
Transfer function of the pole-zero plot, frequency response and its geometrical interpretation. Two-dimensional z-transform.
Discrete Fourier transform and its features. Circular (periodic) convolution and its calculation by means of DFT. Calculation of discrete convolution, method of overlap-add and overlap-save. Two-dimensional DFT.
Fast Fourier transform. Calculation of two real sequences, calculation of double-length real sequence. Fast convolution and correlation.Calculation of inverse DFT by means of direct DFT.
Representation of discrete systems using matrices and signal flow graphs. Mason's rule. State-space canonic structures, serial and parallel forms. Solution of state-space difference equations.
Design of type FIR digital filters, linear phase. Method of windowing, method of frequency response sampling. Optimum uniform rippled filters. Remez algorithm.
Design of type IIR digital filters. Making use of analog prototypes. Frequency transformation. Methods of signal invariance and bilinear transformation.
Multirate systems. Undersampling (decimation) and interpolation. Change in sampling frequency in the form of rational fraction. Filter banks.
Homomorphous processing of signals. Complex and real cepstrums. Application of cepstrums in speech and image processing.
Signal quantization in in discrete systems. Fixed- and floating-point representation of numbers, quantization and rounding. Quantization of transfer function coefficients. Quantization of intermediate results, limit cycles, scaling to reduce arithmetic overflow. Quantization of continuous signal.
Hardware and architecture of microprocessor circuits for digital signal processing. Survey of demands on processing signals from various regions. Harvard architecture. Definition of digital signal processor, classification of digital signal processors by generations, properties of individual generations. Common properties of various types of digital signal processor.
Realization of digital filters and FFT processor in digital signal processors. Development tools, on-chip emulation (DSPlus, DSP56002EVM).

Exercise in computer lab

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Mekyska, Ph.D.

Syllabus

Basic operations in Matlab, generation and representation of discrete signals.
Spectral representation of discrete periodic and non-periodic signals.
Discrete Fourier series and transform and its connection with Fourier series and transform. Fast Fourier transform (FFT).
Discrete linear and periodic convulution and correlation. Calculation using the FFT.
Test No 1.
Modelsof discrete systems, external and state-space description. Transfer function, impulse response, pole-zero plot.
Design of type FIR digital filters, windowing method, Remez algorithm
Desaign of type IIR digital filters.Bilinear transformation and impulse invariance methods.
Test No 2.
Multirate systems, decimation and interpolation.
Complex and real cepstrums. Unwrapping of phase.
Quantization effects in discrete systems. Implementation of algorithms on microprocessors.
Test No 3.