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Last update: T_KG (16.05.2001)
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Last update: T_KG (09.04.2008)
Basic theory of four Fourier-type transforms - Fourier series and transforms od of continuous and discrete time signals. Besides fundamental applications, emphasis is laid on relationships between these transforms. |
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Last update: prof. RNDr. František Gallovič, Ph.D. (27.04.2020)
Podmínkou udělení zápočtu je splnění zápočtového úkolu. Získání zápočtu je podmínkou pro konání zkoušky. |
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Last update: T_KG (19.01.2003)
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Last update: T_KG (11.04.2008)
Lecture + exercises |
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Last update: prof. RNDr. František Gallovič, Ph.D. (06.10.2017)
Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce. |
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Last update: T_KG (03.05.2002)
1. Hilbert space - basic properties. Orthogonal/orthonormal series. Complete systems. General Fourier series, trigonometric and exponential form of F. series.
2. Convergention of Fourier series, Gibs phenomenon. Basic properties of Fourier series.
3. Generalized Fourier series of eigenfuncions and orthogonal polynomials. Multidimensional Fourier series.
4. Fourier theorem. Fourier transform. Sine and cosine transform.
5. Properties of Fourier transform. Multidimensional Fourier transform.
6. Fourier transform of special functions (periodic, Dirac distribution, Heaviside function, signum). Shah function and its properties.
7. Linear filters. Transfer function and impulse response.
8. Hilbert transform - definition, basic properties. Fourier spectra of causal functions. Analytic signals. Instant frequency.
9. Fourier transform of discrete signals. Definition, basic properties. Alias in frequency domain.
10. Fourier series of discrete signals. Definition, basic properties. Alias in time domain.
11. Discrete Fourier transform (DFT). Fast Fourier transform (FFT) algorithm. Fourier interpolation.
12. Fundamentals of time-frequency analysis. Bibliography
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