Course detail

Digital Filters

FEKT-MPC-CIFAcad. year: 2021/2022

The subject deals with basics properties of digital system (transfer function, impulse response, frequency characteristic, stability and causality), design methods of one-dimensional digital filters with finite and infinite impulse response, special types of filters (Hilbert transformer, differentiator), multi-rate system (decimation, interpolation, filter banks.

Learning outcomes of the course unit

Students will be able to:
- Explain the meaning of the parameters of microprocessors and digital signal processors
- Explain the progress of the translation of separate C language source files including linking with other libraries
- Explain the importance of intrinsic functions and use them in their programs
- Explain buffering and double buffering and use them in their programs
- Explain the difference between internal and external digital system descriptions
- Include digital system between FIR and IIR systems
- Check the stability of the digital system
- Prepare the quantized coefficients of a digital system for implementation
- Reformulate a canonical form into another form
- Explain the different types of addressing: linear, modulo, bit-reversed
- Explain the principal methods for the design of FIR and IIR filters
- Apply the method for designing FIR filters and IIR filters by the specified tolerance scheme
- Explain the principle of adaptive filters
- Apply the subsampling or the oversampling ratio of rational numbers
- Explain the principle of filter banks


The basic knowledge of digital signal processing (sampling, representation of discrete-time signals, description of discrete-time systems, etc.) and of microprocessor technology (principles of microprocessors, registers, memory, programming in the C language, debugging) is required. Students should be able to:
- describe the function of basic blocks of the microprocessor (CPU, memory, I / O circuits, etc.)
- explain the basic ANSI C commands
- apply the basic commands of the ANSI C language and implement a simple program
- explain the course of sampling the continuous signal
- explain the importance of the frequency response of a system
- explain the importance of stability
- explain the different number systems
- calculate the binary representation of a number.

Appropriate courses, in which this knowledge can be obtained, are compulsory and optional specialised courses of The teleinformatics study area or equivalent:
- Computers and Programming 2
- Signal and System Analysis
- Digital Circuits and Microprocessors
- Digital Signal Processing .


Not applicable.

Recommended optional programme components

Not applicable.


VÍCH,R., SMÉKAL,Z.: Číslicové filtry. Academia, Praha 2000. ISBN 80-200-0761-X (In Czech) (CS)
MITRA S.K, KAISER J.F.: Handbook for Digital Signal Processing, John Wiley & Sons, New York, 1993. (EN)
SYSEL, P.; SMÉKAL, Z.: Číslicové filtry. Brno: Vysoké učení technické v Brně, 2012. s. 145. ISBN 978-80-214-4454-6 (CS)
SMÉKAL, Z.; SYSEL, P.: Signálové procesory. 1. vydání. Praha: Sdělovací technika, 2006. 283 s. ISBN 80-86645-08-8 (CS)
PROAKIS, J. G.;MANOLAKIS, D. G.:Digital Signal Processing. Prentice Hall: New Jersey, 1996. 3 edition. 966 p. ISBN 0-13-373762-4 (EN)

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in article 7 of the BUT Rules for Studies and Examinations.
Lectures are in the nature explaining the basic principles, methodology of the discipline problems and their solutions.
Practice proceeds on digital signal processor development kits and Matlab.

Assesment methods and criteria linked to learning outcomes

Evaluation of study results follows the Rules for Studies and Examinations of BUT.
2 tests on practical exercises max. 10 marks
Check exercises max. 15 marks
Individual project max. 15 marks
Written examination max. 60 marks

Language of instruction


Work placements

Not applicable.

Course curriculum

1. Digital signal processor architectures, development tools, intrinsic functions.
2. Discrete-time systems, black box description - transfer function, impulse response, stability.
3. State space model of discrete-time systems, signal flow chart, Mason rule.
4. Fixed-point representation effects, modification of structures for fixed-point.
5. Design methods for digital filters with infinite impulse characteristics.
6. Design methods for digital filters with finite impulse characteristics.
7. Design of special filter types - Hilbert transformer, differentiator.
8. Multi-rate system, decimation and interpolation.
9. Filter banks, conditions of perfect reconstruction, quadrature mirror filters.
10. Fraction-octave filters banks, weighting filters.
11. Inverse filtration, optimal Wiener filtration, adaptive filters.
12. Recursive filters design methods, prediction analysis.
13. Introduction to nonlinear systems, homomorphic filtration.


Improving students' knowledge of digital signal processing (DSP) obtained in previous courses. Acquainting students with the basic principles of implementation on technical devices (digital signal processors and microcontrollers). Acquainting students with programming digital signal processors in the C language. Acquainting students with the differences in and problems of implementing digital signal processing methods using floating- and fixed-point arithmetic. Acquainting students with the method of digital filter design.

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

Attendance at lectures is not obligatory
Attendance at computer exercises is obligatory
Self-contained project is obligatory
Written examination is obligatory

Classification of course in study plans

  • Programme MPC-TIT Master's, any year of study, summer semester, 6 credits, elective

  • Programme MPC-AUD Master's

    specialization AUDM-ZVUK , 1. year of study, summer semester, 6 credits, compulsory-optional
    specialization AUDM-TECH , 2. year of study, summer semester, 6 credits, compulsory-optional

Type of course unit



26 hours, optionally

Teacher / Lecturer

Exercise in computer lab

39 hours, compulsory

Teacher / Lecturer