Course detail

Digital Filters

FEKT-CCIFAcad. year: 2009/2010

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 digital signal 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

English

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 student will be able to design independently basic types of linear, adaptive and non-linear digital filters, to perform quantizing and realize it by technical tools.S/he will be able to analyze their properties and use them in telecommunication applications.

Prerequisites

The fundemental knowledge on the digital signal processing and Matlab utilization are requested.

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

test practice max. 7 marks
check exercises max. 8 marks
self-dependent project max. 15 marks
written examination max. 70 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.
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 number. Quantization effects on transfer function, on frequency response, on zeros and poles location, limit cycles.
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, linear phase. 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 response.
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.
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

The subject covers the whole range of the 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

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

lectures are not duly
computer exercise are duly
self-dependent project is duly

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

MITRA S.K, KAISER J.F.: Handbook for Digital Signal Processing, John Wiley & Sons, New York, 1993. (EN)

Recommended reading

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

Classification of course in study plans

  • Programme EEKR-BC Bachelor's

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

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

doc. Ing. Petr Sysel, Ph.D.

Syllabus

Properties of one-dimensional digital filters (DF). Stages of DF design and realization. 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.
The z-transform, convergence area and properties. Inverse z-transform and its calculation. Solution of differential equations with the aid of the z-transform.
Reakization 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. Optimum method of uniformly rippled approximations, the Remez algorithm. Method of window sequences and sampling frequency characteristic.
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.
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.
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.
Quantizing effects in DF. Digital number representation with limited word length, fixed and floating point arithmetic, dynamic representation range.
Quantization of transfer function coefficients, quantization of intermediate results of arithmetic operations. Quantization of input signal. Limiting the effect of quantization.
Harvard architectire of microprocessor for digital filtering. Harvard architecture. Definition of digital signal processor, generations and properties.
Implementation of DF on digital signal processors. Development tools, on chip emulation (DSPlus, DSP56002EVM).

Laboratory exercise

26 hours, compulsory

Teacher / Lecturer

doc. Ing. Petr Sysel, Ph.D.

Syllabus

Design of type FIR DF by the window method as specified, for these frames: rectangular, Hamming's, Blackmann's, and Kaiser's. Calculation is performed by both using definition relations and comparing via available programs
Design of type IIR DF according to Tables for the given specification, by the method of bilinear transformation (suitable type of approximation is chosen such that the specified conditions are fulfilled).
For the proposed DF of FIR and IIR types the quantization of transfer function coefficients is performed for a given number of bits and transfer function distribution into cascade or parallel structure. Scaling coefficients between sections are proposed such as to prevent reading errors.
For both types of DF the program is written in the assembler of digital signal processor. Via simulation with the discrete harmonic signal applied to the input of DF model for both pass and stop bands the correct function of DF is tested.
Demonstration of spectral analyzer and other applications on DSP56002EVM and DSP56307EVM.
The following programs or program files are available for DF design: Matlab version 5.3, toolboxes, bcaprox.exe (Butterworth and Chebyshev approximations combined with bilinear transformation and quantization of transfer function coefficients), edifi.exe (Cauer approximation - elliptic filters - combined with bilinear transformation and coefficient quantization), afir.exe (weight sequence method for the Kaiser window and quantization of transfer function coefficients), firq.exe (Remez algorithm for optimum FIR filter design). Available for implementation on digital signal processor are: DSPlus (integrated environment for processors of the DSP56000 Motorola family, Goldwave (input and output files).