1. Classify signals and systems by type
2. State and explain the sampling theorem
3. Analyze signals using signal decomposition and signal spectrum
4. Analyze systems using transfer functions and frequency responses
5. Explain three fundamental problems of signal processing: filtration, reconstruction and prediction
6. Analyze a concrete signal filtration problem and prepare a filter specification
7. Design and implement a digital filter using a computer
8. Explain what the fast Fourier transform is and list its applications

Lectures present theoretical concepts.

Recitations include solving practical tasks and discussing solving procedures.

Laboratory exercises introduce to students how computers are used for signal processing.

1. Introduction. Signals. Classification of signals. Signal decomposition.
2. Fourier transforms (DFT, DTFT, CTFT). Signal spectrum.
3. Sampling and reconstruction. The sampling theorem.
4. Window functions and spectral analysis. Discrete cosine transform (DCT-II).
5. Systems. Classification of systems. Linear time invariant systems. The convolution sum.
6. Laplace transform. Z transform. Transfer function and frequency response.
7. Equivalence of continuous and discrete systems. Euler and reversed Euler methods. Bilinear transform.
8. Midterm exam
9. Three fundamental problems: filtering, reconstruction and prediction. Digital filters and signal filtering.
10. Filter specification. Response to composite signal. Stability and steady-state response. Phase and group delay. Classification of digital filters.
11. FIR filtes and linear phase systems. Computer aided design of amplitude-selective linear-phase FIR filters.
12. IIR filters and minimum phase systems. Computer aided design of amplitude-selective minimum-phase IIR filters.
13. Fast Fourier transform and its applications. Linear and circular convolution. Efficient computation of the convolution sum.
14. Filter realizations. Fixed-point arithmetic. Digital signal processors.
15. Final exam