Fundamentals of Signal Processing

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

Course title

Fundamentals of Signal Processing

Lecture type


Course code






Lecturers and associates

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.
Advantages and drawbacks.
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.

Required reading

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
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