 Study

# Computing

## Fundamentals of Signal Processing

• Class 45
• Practice 30
• Independent work 75
Total 150

### Course title

Fundamentals of Signal Processing

Elective

183447

5

5

### Course objectives

Definition of signals and systems; Classification of signals and systems; Signals and systems parameters; Modeling of signals and systems; Continuos time Fourier series (CTFS); Continuos time Fourier transform (CTFT); Discrete time Fourier series (DTFS); Discrete time Fourier transform (DTFT).
Nyquist frequency; Aliasing in time and frequency domain; Interpolation; Signal dimensionality.
Symmetric and periodic signal extension; Discrete cosine transform (DCT): 4 variants.
Impulse response of the LTI systems; Convolution sum and integral; Linear differential and difference systems.
Frequency response; Definition, similarities to Laplace transform; Properties; Transfer function; Use in solving LTI systems response.
Problem definition.
Midterm exam.
Types and structures.
Linear, periodic and circular convolution.
Window based design; Parks Mcclellan and Remez.
Types and structures.
Discrete Fourier transform (DFT); Cooley-Tukey algorithm; Radix-2 case; Butterfly structure; Data reordering; Bit reversal; In-place algorithm.
Modified DCT and DCT filterbanks; Scalar and vector quantization.
Final exam.

Paolo Prandoni, Martin Vetterli (2008.), Signal Processing for Communications, EPFL Press
Sanjit Kumar Mitra (2010.), Digital Signal Processing: A Computer Based Approach, McGraw-Hill
Alan V. Oppenheim, Ronald W. Schafer (2010.), Discrete-Time Signal Processing, Pearson
John G. Proakis, Dimitris G. Manolakis (2007.), Digital Signal Processing, Pearson

#### Minimal learning outcomes

• Classify signaly and systems by type
• Explain the importance of signal processing in computing, electronics, control engineering and telecommunications
• State and explain the Nyquist-Shannon sampling theorem
• Analyze signals using their spectrum
• Analyze systems using theirs transfer function and frequency response
• Explain the equivalence between time continuous and time discrete systems
• Explain signal filtration
• Design a basic digital filter using a computer
• Explain what the fast Fourier transform is and list its applications