Course detail

Multirate Systems

FEKT-LMUTAcad. year: 2010/2011

A systems for sampling-rate conversion. Multirate digital filters and fast algorithms of filtering. Time-frequency transforms, the wavelet transform (WT). Continuous-time wavelet transform (CTWT), discrete-time wavelet transform (DTWT), dyadic DTWT, packet DTWT. DTWT and its relation to multirate filter banks. Perfect reconstruction filter banks. The orthogonal and biorthogonal DTWT. Wavelet-based filtering of the signals and images. Complex WT and its applications. Separable and nonseparable 2D wavelet transform. Wavelet-based compression of signals and images.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. Ing. Jiří Kozumplík, CSc.

Department

Department of Biomedical Engineering (UBMI)

Learning outcomes of the course unit

Design and implementation of systems for sampling rate conversion and multirate digital filters with high computational efficiency. Design and implementation of wavelet transforms (WT), applications of WT for filtering, compression and analysis of signals and images.

Prerequisites

The subject knowledge on the Bachelor´s degree level is 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

Requirements for completion of a course are specified by a regulation issued by the lecturer responsible for the course and updated for every.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The course provides in-depth treatment of sampling-rate conversion and its applications to multirate digital signal processing, including the implementation of digital filters. The second part provides a deeper study of multirate filter banks, 1D and 2D wavelet transforms, wavelet-based filtering and compression of signals and images.

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.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Proakis,J.G., Manolakis,D.G.: Digital Signal Processing. Principles, Algorithms and Applications. (Second Edition). Macmillan, 1992. (EN)

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme EEKR-ML Master's

    branch ML-BEI , 1 year of study, summer semester, elective specialised

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

doc. Ing. Jiří Kozumplík, CSc.

Syllabus

Signal decimation by an integer factor D, signal interpolation by an integer factor I, spectral representation of the decimated and interpolated signals.
Sampling-rate conversion by a rational factor I/D, multistage implementations of sampling-rate conversion of signals. Sampling-rate conversion by an arbitrary factor.
Direct-form structures and polyphase structures of decimators and interpolators.
Multirate digital filters and fast algorithms of filtering. Implementation of multirate filter banks.
Time-frequency transforms, the wavelet transform (WT). Continuous-time wavelet transform (CTWT)
Discrete wavelet transform (DWT), discrete-time wavelet transform (DTWT), dyadic (fast) DTWT, packet DTWT.
WT and its relation to multirate filter banks. Perfect reconstruction filter banks. Quadrature mirror filters (QMF), half-band filters.
Implementation of the orthogonal and biorthogonal DTWT, lifting.
Wavelet-based filtering of the signals. Decimated and undecimated WT.
Complex WT (CWT), its implementation and applications.
Wavelet-based compression of signals. Lossy and loss-less compression.
Separable and nonseparable 2D wavelet transform. Wavelet-based compression and filtering of images.
Standards MPEG and JPEG2000.

Exercise in computer lab

26 hod., compulsory

Teacher / Lecturer

doc. Ing. Jiří Kozumplík, CSc.

Syllabus

Sampling rate conversion of discrete-time signals in the frequency domain and in the time domain.
Design and implementation of systems for sampling rate conversion (individual projects solution).
Design and implementation of systems for sampling rate conversion (individual projects solution).
Multirate digital filters.
Design and implementation of the multirate digital filters (individual projects solution).
Design and implementation of the multirate digital filters (individual projects solution).
Realization of DTWT and inverse DTWT by use of filter banks.
Implementation of the orthogonal and biorthogonal (dyadic and packet) DTWT (individual projects solution).
Implementation of the orthogonal and biorthogonal (dyadic and packet) DTWT (individual projects solution).
Introduction to the MATLAB Wavelet Toolbox.
Wavelet-based filtering and compression of signals by use of the MATLAB Wavelet Toolbox (individual projects solution).
Wavelet-based filtering and compression of signals by use of the MATLAB Wavelet Toolbox (individual projects solution).
Separable and nonseparable 2D wavelet transform.