Course detail

Digital Filters

FEKT-KCIFAcad. year: 2010/2011

The subject covers the whole range of the analysis and design of one-dimensional digital filters, from entering differential equations of a linear discrete system with one input and one output, through methods of designing linear and non-linear digital filters up to the realization by digital hardware tools. Properties of one-dimensional digital filters (DF). Transfer function, impulse response, pole-zero plot. Stability and causality. Frequency properties. Realization structurs of DF. Analysis of DF properties, using signal flow graphs and matrices. Quantizing effects in DF. Implementation of DF on processors. Design methods for type FIR and type IIR digital filters. Adaptive DF. Multirate digital filters. Filter banks and polyphase filters. Wavelet transform and principle of multiple resolution. Homomorphous signal processing and non-linear digital filters.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Ing. Petr Sysel, Ph.D.

Department

Department of Telecommunications (UTKO)

Learning outcomes of the course unit

The graduate gains experience with the simulation of digital filters in computing environments Matlab and Octave, experience with application of design methods of digital filters according to a particular frequency or time requirements, and experience with the practical implementation of digital filters in processor with fixed point arithmetic.

Prerequisites

Are required basic knowledge of digital signal processing obtained as a compulsory course in the Signals and systems analysis.

Co-requisites

Not applicable.

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

Solution of the seven homeworks 40 marks
Written examination 60 marks

Course curriculum

1. Classification and fundamental properties of digital systems. Description of digital filters by difference equations, Z transform of difference equation. Definition of transfer function, definition of zeros and poles. Impulse response.
2. Causal and stability of linear time invariant systems, stability test. Definition of frequency response, digital filters as basic frequency-selective filters, zero and pole location. Linear phase frequency response.
3. Structures for realization for digital filters, first and second direct form, first and second transposed form. Signal flow graphs for digital filters description, analyses of signal flow graph by Mason's rule.
4. Fixed- and floating-point representation of numbers, accuracy and dynamic range, representation of negative numbers. Quantization effects on transfer function, on frequency response, on zeros and poles location. Limit cycles. Analysis of quantization errors.
5. Preparation of transfer functions for implementation in technical devices, dividing of high-order transfer function into second order sections. Hardware for implementation of digital filters, examples of implementation of FIR and IIR filters.
6. Design of FIR type digital filters. Method of windowing, method of frequency response sampling.
7. Optimum uniform rippled filters, alternation theorem, Remez's algorithm. Design of special kind of digital filters - differentiators, Hilbert's transformers.
8. Design of IIR digital filters. Making use of analog prototypes. Methods of bilinear transformation and impulse invariance.
9. Computer based method of IIR digital filters design, least-squares method. Inverse filtering.
10. Optimal Wiener filtration, Wiener-Hopf equation. Adaptive filters, LMS algorithms, RLS algorithms.
11. Multirate systems, decimation and interpolation, change in sampling frequency in the form of rational fraction.
12. Filter banks, perfect reconstruction condition, quadrature mirror filters. Wavelet transform.
13. Nonlinear digital filters, polynomial digital filters, filters based on sorting. Homomorphous filtering, real and complex cepstrum.

Work placements

Not applicable.

Aims

To deepen the basic knowledge of digital signal processing techniques acquired in the compulsory course "Signals and systems analysis" primarily on practical experience with implementation of digital filters, to reduce the effects of quantization on the characteristics of digital filters, and design methods using digital filters.

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

Tutorials are not duly
Computer exercise are duly
Surrender of separate tasks is duly

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

VÍCH,R., SMÉKAL,Z.: Digital Filters (Číslicové filtry). Academia, Praha 2000. ISBN 80-200-0761-X (In Czech) (CS)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-BK Bachelor's

    branch BK-TLI , 3. year of study, winter semester, optional specialized

  • Programme EEKR-CZV lifelong learning

    branch ET-CZV , 1. year of study, winter semester, optional specialized

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

doc. Ing. Petr Sysel, Ph.D.

Syllabus

1. Properties of one-dimensional digital filters (DF). Linear differential equation and its solution. Transfer function, impulse response, pole-zero plot. Stability and causality, frequency properties. Systems of the type of FIR and IIR and their basic properties.
2. Realization structures of DF. Avalysis of DF properties, using matrices and signal flow graphs, Mason's Gain Rule. Canonical and non-canonical realization structures. Design methods for type FIR digital filters. Quantization of transfer function coefficients, quantization of intermediate results of arithmetic operations. Quantization of input signal. Limiting the effect of quantization. Optimum method of uniformly rippled approximations, the Remez algorithm. Method of window sequences and sampling frequency characteristic.
3. Design methods for type IIR filters. Design based on analog prototype, method of signal invariance, method of bilinear transformation. Wavelet digital filters. Design by the LSM.
4. Adaptive DF. Preconditions of adaptive algorithm selection. Adaptive filter structures, type LMS alllgorithms, their application. Multirate Digital Signal Processing. Decimation, interpolation. Change in the sampling frequency in the form of rational fraction. Application of these systems in digital filtering.
5. Filter banks and poly-phase filters. Wavelet transform and principle of multiple resolution. Methods of signal analysis and compression by filter bank. Homomorphous signal processing and non-linear digital filters. Generalized principle of superposition. Complex and real cepstrum. Cepstrum application in speech and image processing.

Laboratory exercise

26 hours, compulsory

Teacher / Lecturer

doc. Ing. Petr Sysel, Ph.D.

Syllabus

1. Implementation structures of digital filters.
2. Design methods of digital filters.