Digital Signal Processing
FEKT-BPC-CZSAcad. year: 2018/2019
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 in digital signal processors.
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
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.
Recommended optional programme components
Recommended or required reading
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)
MIŠUREC,J., SMÉKAL,Z. Číslicové zpracování signálů. Skriptum FEKT VUT v Brně, 2012. (CS)
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.
Language of instruction
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.
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.
Classification of course in study plans
- Programme BPC-AUD Bachelor's
- Programme BPC-TLI Bachelor's, 2. year of study, summer semester, 5 credits, compulsory-optional
- Programme BPC-MET Bachelor's, 3. year of study, summer semester, 5 credits, compulsory-optional