Digital Filters

A tantárgy neve magyarul / Name of the subject in Hungarian: Digitális szűrők

Last updated: 2009. október 30.

Tantárgy lejárati dátuma: 2015. június 30.

Budapest University of Technology and Economics
Faculty of Electrical Engineering and Informatics

Electrical Engineering

Specialization Embedded Information Systems

M.Sc. program

Obligatory elective subject

Course ID Semester Assessment Credit Tantárgyfélév
VIMIM278 2 2/1/0/v 4  
3. Course coordinator and department Dr. Sujbert László,
Web page of the course
4. Instructors László Sujbert, Ph.D.
6. Pre-requisites
Signal processing
7. Objectives, learning outcomes and obtained knowledge The subject deals with the analysis, design and implementation of linear, time-invariant discrete-time filters. Application of digital filters requires deep knowledge of many theoretical and practical details. These problems are usually not discussed in detail in other courses. The aim of the subject is to give the most detailed review of the topic, from the mathematical basics to the programming methods. Although the learning of the theoretical background is inevitable, it is also an important goal to deliver practical skills. Therefore the review of the corresponding Matlab functions, and the digital signal processor based support of the implementation are also included in the program of the subject.



Students fulfilled the requirements of the subject are familiar with the possibilities of the application of digital filters; they can carry out the complete analysis of a filter with given transfer function; they know the most important design methods for finite and infinite impulse response filters. Having the high-level theoretical knowledge the students can use the high-level software support (Matlab functions); they can select the appropriate structure for the implementation. The students fulfilled the course are able to implement digital filters, especially using digital signal processors.


8. Synopsis Digital Filtering Problems. Digital filtering in information processing systems. Comparison of analog and digital filters.


Analysis and Synthesis Methods. Determination of the amplitude and phase response using analytic and numeric methods. Sensitivity analysis. Noise analysis. synthesis of linear networks. Analog to discrete transform of transfer functions. Matlab support.


Design of IIR Filters. Classical approximation methods: Butterworth, Chebishev, inverse Chebishev, elliptic filters. Frequency transforms. Design with least squares method. Design in the time domain. Filter order estimation. Matlab support.


Design of FIR Filters. The role of linear phase filters. Connection between the amplitude response and the impulse response. Design with frequency sampling. Design with windowing. Design with the Remes algorithm. Filter order estimation. Matlab support.


Special Digital Filters. Hilbert transformers. Gauss filters. Nonlinear filters, median filters. Matlab support.


Implementation. Problems of implementation: quantization, overflow, instability, limit cycles, noise. Digital filtering in common microprocessors and digital signal processors. Computational demand. Support offered by signal processors. Programming methods. Effective on-line and off-line methods. Signal processor support.


Implementation of FIR Filters. Transverse structure. Algorithms based on fast convolution. Filtering in the transform domain. Matlab and signal processor support.


Implementation of IIR Filters. Direct structure. Decomposition of the transfer function into second order blocks: cascade and parallel structure. Ordering of the blocks. Lattice structures. Wave digital filters. Resonator-based filters. Matlab and signal processor support.


9. Method of instruction

2 hours/week lectures and 1 hour/week exercise.

10. Assessment

In the class period: 1 homework

In the examination period: written exam

Exam before the examination period: not available

11. Recaps The homework can be submitted in the rectification period.
12. Consultations By appointment.
13. References, textbooks and resources

Simonyi Ernő, "Digitális szűrők. A digitális jelfeldolgozás alapjai", Műszaki Könyvkiadó, Budapest, 1984.

Parks, T. W., C. S. Burrus, "Digital Filter Design", John Wiley & Sons, New York, etc. 1987.

14. Required learning hours and assignment
Preparation for test
Learning of prescribed matters10
Preparation for exam48
15. Syllabus prepared by László Sujbert, Ph.D.
Comments The name of the subject in Hungarian: Digitális szűrők