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Applets of Integral and Discrete Transforms
| Type of study | Doctoral |
|---|---|
| Language of instruction | English |
| Code | 470-6103/02 |
| Abbreviation | VSIDT |
| Course title | Applets of Integral and Discrete Transforms |
| Credits | 10 |
| Coordinating department | Department of Applied Mathematics |
| Course coordinator | doc. Ing. David Horák, Ph.D. |
Osnova předmětu
Lectures:
Introduction to integral transforms. Linear spaces, norm, scalar product. Hilbert space. Convergence of series and integrals. Orthogonal systems, series and function convolutions.
Laplace and Fourier transforms. Inverse transforms. Fourier-Laplace transform.
Discrete transforms. Discrete L-transform (Dirichlet series). Discrete Fourier transform. Discretization errors. FFT algorithm.
Distribution, Dirac's impuls, L-image, F-image of distribution. Distribution reprezentation. Convolution as a general integral transform. Inverse convolution. Decomposition. Window function.
Introduction to harmonic analysis. Shanonn-Kotelnik theorem. Mathematical filters, Gabor's transform. Window Fourier transform. Regularization.
Generalized Fourier series and wavelets (time-frequency analysis). Wavelet bases, properties, construction. Continuous wavelet transform. Discrete wavelet transform. Multiresolution decomposition (MRA). Pyramid's algorithm. Packet decomposition. Data compression, signal reconstruction and other applications.
Software for discrete transforms.
Introduction to integral transforms. Linear spaces, norm, scalar product. Hilbert space. Convergence of series and integrals. Orthogonal systems, series and function convolutions.
Laplace and Fourier transforms. Inverse transforms. Fourier-Laplace transform.
Discrete transforms. Discrete L-transform (Dirichlet series). Discrete Fourier transform. Discretization errors. FFT algorithm.
Distribution, Dirac's impuls, L-image, F-image of distribution. Distribution reprezentation. Convolution as a general integral transform. Inverse convolution. Decomposition. Window function.
Introduction to harmonic analysis. Shanonn-Kotelnik theorem. Mathematical filters, Gabor's transform. Window Fourier transform. Regularization.
Generalized Fourier series and wavelets (time-frequency analysis). Wavelet bases, properties, construction. Continuous wavelet transform. Discrete wavelet transform. Multiresolution decomposition (MRA). Pyramid's algorithm. Packet decomposition. Data compression, signal reconstruction and other applications.
Software for discrete transforms.
E-learning
Consultation through MS Teams.
Povinná literatura
G.James and D.Burley, P.Dyke, J.Searl, N.Steele, J.Wright: Advanced Modern Engineering Mathematics,Addison-Wesley Publishing Company, 1994.
William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0.
William L. Briggs, Van Emden Henson: An Owner's Manual for the Discrete Fourier Transform, SIAM, 1995, ISBN 0-89871-342-0.
Doporučená literatura
Michael W. Frazier: An introduction to wavelets through Linear Algebra, Springer,1999, ISBN 0-387-98639-1.