Skip to main content
Skip header
Terminated in academic year 2011/2012

Discrete Transforms

Type of study Follow-up Master
Language of instruction Czech
Code 470-4303/01
Abbreviation DT
Course title Discrete Transforms
Credits 5
Coordinating department Department of Applied Mathematics
Course coordinator doc. Ing. David Horák, Ph.D.

Subject syllabus

Lectures:

Orthogonal discrete systems. Distributions and Delta-operator.
Systems of convolution equations. Deconvolution.
Discrete Laplace transform and two-side Laplace transform.
Discrete Fourier transform, FFT.
Inverse transforms and problems of the discrete inverse transforms. Regularization. Applications.
Windowed Fourier transforms. Applications.
Wavelet transforms. Discrete wavelet transform. Multiresolution. Analysis. Applications.

Exercises:
Preparing to computer exercises.


Projects:
Project and its presentation on the realization of a particular problem.


Computer labs:

Introduction to MATLAB.
Orthogonal discrete systems (Haar, Walsh, Rademacher etc.).
Numerical analysis of signals using discrete Fourier transform.
FFT algorithm and implementation.
Windowed Fourier transforms. Algorithm and implementation.
Discrete wavelet transform. Algorithm and implementation.
Applications of mentioned algorithms in technical problems.

Literature

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Bachman G., Narici L., Becktenstein E.: Fourier and wavelet analysis, Springer, 2000.

Advised literature

G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
Bachman G., Narici L., Becktenstein E.: Fourier and wavelet analysis, Springer, 2000.
W.L.Briggs, V.E. Henson: The DFT, SIAM, 1995.