Course detail

Digital Signal Processing

FEKT-BKC-CZSAcad. year: 2020/2021

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. Basics of designing 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

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Mišurec, CSc.

Department

Department of Telecommunications (UTKO)

Learning outcomes of the course unit

Students of the course Digital signal processing will understand the basic algorithms for digital signal processing and will be able to independently apply and model the basic functions of digital processing in Matlab. They will have a basic idea of the implementation of the algorithms on microprocessors and digital signal processors. Students will primarily become familiar with the terms:
- Discrete signals and their description
- Discrete systems and their description
- Status of description systems
- Z-Transform and its application in solving digital systems
- Frequency analysis of discrete signals
- Discrete system - frequency selective filter
- Discrete Fourier transform
- Technical means of digital signal processing

Prerequisites

Students should have basic knowledge of mathematics and physical description of the signal, which they obtain in the obligatory courses in their previous study. Taking those courses is not a prerequisite for signing up for this course.

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 on 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.
The exam is focused on verifying students’ orientation in the basic problems of digital processing, their description, calculation methods, characterization of system analysis, and synthesis of digital systems.

Course curriculum

1. Discrete signals - sampling and reconstruction of signals, basic single and multidimensional discrete signals and operations with them.
2. Frequency analysis of discrete signals - definition of DFT, DFT properties, vector form of DFT, fast FT calculation algorithm.
3. Discrete systems - initial conditions, representation of discrete systems using block diagrams and signal flow graphs.
4. Transformation Z and its use for solving discrete systems, the relationship between FT discrete signal and bilateral Z transformation.
5. Discrete systems - classification of discrete systems, linear time-invariant discrete system (LTI), connection of partial discrete LTI systems, causality and stability of LTI discrete system, discrete LTI systems of IR and IIR type.
6. State description of linear time-invariant discrete system, implementation structures.
7. Frequency characteristics of a linear time-invariant discrete system. Linear invariant discrete system as frequency filter - LPF, HPF, digital resonator, BPF, notch filter, BRF, comb filter, all-pass filter.
8. Basic methods of discrete system design according to frequency characteristic.
9. Inverse systems and deconvolution - discrete system inversibility, geometric interpretation of frequency characteristics, linear invariant discrete system with minimal, maximum and mixed phase, kepstrum, homomorphic deconvolution.
10. Expression of fixed and floating-point numbers, effect on stability and other features of the discrete LTI system.
11. Modification of the transfer function with regard to quantization effects, subdivision into sub-sections.
12. Implementation of digital signal processing using signal processors.
13. Architecture of digital signal processors.

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. Particularly emphasized are methods for describing digital systems, especially digital filters. The course 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

MIŠUREC,J., SMÉKAL,Z. Číslicové zpracování signálů. Skriptum FEKT VUT v Brně, 2012. (CS)
MITRA,S.K., Digital Signal Processing-A Computer-Based Approach. The McGraw-Hill Companies, Inc. New York 1998 (EN)
OPPENHEIM, A.L., SCHAFER, R.W., Digital Signal Processing, Prentice-Hall, Inc. New Jersey, 1995. (EN)
SMÉKAL,Z., VÍCH,R., Zpracování signálů pomocí signálových procesorů. Radix spol.s.r.o., Praha 1998. (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BKC-MET Bachelor's 2 year of study, summer semester, compulsory-optional

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

prof. Ing. Jiří Mišurec, CSc.

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.