1. Basic types of signals. Basic signal transforms.
2. Signal spectrum, Fourier series. Fourier transform.
3. Spectra of basic types of signals.
4. Basic signal transforms and their influence on the signal spectrum.
5. 1D and 2D ideal sampling functions, sampling theorem.
6. Reconstruction of signals by ideal low-pass filter. Reconstruction with a real filter.
7. 1D and 2D discrete Fourier transform and discrete cosine transforms, their properties and comparison.
8. Short-term Fourier transform, spectrogram.
9. Window functions and their spectral properties.
10. Filtration and its influence on the signal spectrum. Telephone speech band.
11. 2D discrete Fourier transform and its relation to optical imaging systems. Airy shape.
12. Discrete wavelet transform DWT as filtering. Filter banks.
13. Multidimensional signals, their interpretation, processing and display. Principal component analysis.
The teaching format is chosen so that students, through the modeling of phenomena from everyday experience, get to the mathematical relationships that describe these phenomena and then learn to use these relationships retrospectively.
2. Signal spectrum, Fourier series. Fourier transform.
3. Spectra of basic types of signals.
4. Basic signal transforms and their influence on the signal spectrum.
5. 1D and 2D ideal sampling functions, sampling theorem.
6. Reconstruction of signals by ideal low-pass filter. Reconstruction with a real filter.
7. 1D and 2D discrete Fourier transform and discrete cosine transforms, their properties and comparison.
8. Short-term Fourier transform, spectrogram.
9. Window functions and their spectral properties.
10. Filtration and its influence on the signal spectrum. Telephone speech band.
11. 2D discrete Fourier transform and its relation to optical imaging systems. Airy shape.
12. Discrete wavelet transform DWT as filtering. Filter banks.
13. Multidimensional signals, their interpretation, processing and display. Principal component analysis.
The teaching format is chosen so that students, through the modeling of phenomena from everyday experience, get to the mathematical relationships that describe these phenomena and then learn to use these relationships retrospectively.