Course detail

# Digital Signal Processing

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.

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.

Recommended optional programme components

Not applicable.

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.
SMÉKAL,Z., VÍCH,R., Zpracování signálů pomocí signálových procesorů. Radix spol.s.r.o., Praha 1998.
MIŠUREC,J., SMÉKAL,Z. Číslicové zpracování signálů. Skriptum FEKT VUT v Brně, 2012.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

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

Czech

Work placements

Not applicable.

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, causality and stability of time-invariant systems, FIR and IIR systems.
5. State diagram of linear time-invariant system.
6. Z- transform and its application.
7. Frequency analysis of discrete signals – discrete time Fourier series, 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 the Z- transform.
10. Inverse systems and deconvolution - reciprocal discrete system, geometric interpretation of frequency response, linear time-invariant discrete system with minimum, maximum and mixed-phase homomorphic deconvolution.

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.

Classification of course in study plans

• Programme EEKR-BK Bachelor's

branch BK-MET , 2. year of study, summer semester, 5 credits, optional specialized

• Programme EEKR-CZV lifelong learning

branch ET-CZV , 1. year of study, summer semester, 5 credits, optional specialized

#### Type of course unit

Lecture

26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

26 hours, compulsory

Teacher / Lecturer