Fundamentals of Signal Processing

Learning Outcomes

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

Forms of Teaching


Lectures are held once weekly in a three hour session.


Recitations are held ten times during the semester in one hours sessions.


Laboratory excersises are held six times during the semester in three hours sessions.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 50 % 15 % 50 % 15 %
Homeworks 0 % 5 % 0 % 0 %
Mid Term Exam: Written 0 % 30 % 0 %
Final Exam: Written 0 % 30 %
Final Exam: Oral 20 %
Exam: Written 50 % 50 %
Exam: Oral 35 %

Mandatory prerequisites for oral exams are achieving at least 50% of points on midterm and final exam combined, or on the written part of a regular exam. A minimum of 5 points is required to pass the final oral exam. A minimum of 15 points is required to pass the regular oral exam.

Week by Week Schedule

  1. 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).
  2. Nyquist frequency; Aliasing in time and frequency domain; Interpolation; Signal dimensionality.
  3. Symmetric and periodic signal extension; Discrete cosine transform (DCT): 4 variants.
  4. Impulse response of the LTI systems; Convolution sum and integral; Linear differential and difference systems.
  5. Frequency response; Definition, similarities to Laplace transform; Properties; Transfer function; Use in solving LTI systems response.
  6. Problem definition.
  7. Advantages and drawbacks.
  8. Midterm exam.
  9. Types and structures.
  10. Linear, periodic and circular convolution.
  11. Window based design; Parks Mcclellan and Remez.
  12. Types and structures.
  13. Discrete Fourier transform (DFT); Cooley-Tukey algorithm; Radix-2 case; Butterfly structure; Data reordering; Bit reversal; In-place algorithm.
  14. Modified DCT and DCT filterbanks; Scalar and vector quantization.
  15. Final exam.

Study Programmes

University undergraduate
Computing (study)
Elective Courses (5. semester)
Electrical Engineering and Information Technology (study)
Elective Courses (5. semester)


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


ID 183447
  Winter semester
L1 English Level
L1 e-Learning
45 Lectures
10 Exercises
20 Laboratory exercises
0 Project laboratory

Grading System

87 Excellent
75 Very Good
64 Good
51 Acceptable