457-0302/01 – Discrete Transforms (DT)
| Gurantor department | Department of Applied Mathematics | Credits | 5 |
| Subject guarantor | doc. Ing. David Horák, Ph.D. | Subject version guarantor | doc. Ing. David Horák, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | 3 | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2003/2004 | Year of cancellation | 2009/2010 |
| Intended for the faculties | FEI | Intended for study types | Master |
Subject aims expressed by acquired skills and competences
To give students knowledge of concepts and numerical algorithms of integral and discrete transformations.
Teaching methods
Summary
Discrete transformations are the tools of effective numerical solution of technical problems. The subject contains classical and modern theory and algorithms.
Compulsory 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.
Recommended 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.
Way of continuous check of knowledge in the course of semester
Verification of study:
Test of discrete Fourier transform and distribution - max. 10 points.
Computer test of using of implemented algorithms - max. 10 points.
Five computer examples from numerical exercises - max. 10 points.
Individual project - max. 20 points.
Conditions for credit:
Two tests - max. 20 points.
One individual project and presentation - max. 20 points.
Five computer examples from numerical exercises - max. 10 points.
Maximal number of points from exercises - 50 points.
Minimal number of points from exercises - 25 points.
E-learning
Other requirements
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
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.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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