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Fourier series. Fourier transform. Filters. Hilbert transform. Analytic signals. Fourier transform and Fourier series of discrete signals. Dicrete Fourier transform. Aliasing. Fast Fourier transform. Time-frequency analysis.
Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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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. Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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Podmínkou udělení zápočtu je aktivní účast na cvičeních. Povaha kontroly studia předmětu vylučuje opravné termíny zápočtu. Získání zápočtu je podmínkou pro konání zkoušky. Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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Lecture + exercises Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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Zkouška je ústní, požadavky odpovídají sylabu v rozsahu prezentovaném na přednášce. Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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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
Last update: Gallovič František, prof. RNDr., Ph.D. (06.06.2019)
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