### Fundamentals of Signal Processing

#### Course Description

In this course students gain fundamental insights related to signals processing with the aim of acquiring knowledge that will enable them to understand the methods and the algorithms of signal processing. The following topics are covered: Signals. Classification of signals. Fourier transform and signal spectrum. Sampling and reconstruction. Nyquist-Shannon sampling theorem. Systems. Classification of systems. Linear time invariant systems. The convolution sum. Laplace and Z transforms. Transfer function and frequency response. Equivalence of continuous and discrete systems. Euler and reversed Euler methods. Bilinear transform. Digital processing of analog signals. Filtering. Phase and group delay. Classification of digital filters. Linear-phase filters. All-pass filters. Amplitude-selective filters. Computer aided design of amplitude-selective filters. Fast Fourier transform and its applications. Efficient computation of the convolution sum. Digital signal processor. Fixed-Point Artimetics. Signal quantization.

#### 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

Lectures present theoretical concepts.

Exercises

Recitations include solving practical tasks and discussing solving procedures.

Laboratory

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

#### 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 %
##### Comment:

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, and at least 50% on laboratory exercises.
A minimum of 4 points is required to pass the final oral exam.
A minimum of 8 points is required to pass the regular oral exam.

#### Week by Week Schedule

1. Introduction. Signals. Classification of signals. Signal decomposition.
2. Fourier transforms (DFT, DTFT, CTFT). Signal spectrum. Sampling and reconstruction. The sampling theorem.
3. Window functions and spectral analysis. Discrete cosine transform (DCT-II).
4. Systems. Classification of systems. Linear time invariant systems. The convolution sum.
5. Laplace transform. Z transform. Transfer function and frequency response.
6. Equivalence of continuous and discrete systems. Euler and reversed Euler methods. Bilinear transform.
7. Digital processing of analog signals. Filtering.
8. Midterm exam
9. Phase and group delay. Linear-phase systems. All-pass systems.
10. Classification of digital filters. Amplitude-selective filters. Phase correctors.
11. Computer aided design of amplitude-selective FIR filters.
12. Computer aided design of amplitude-selective IIR filters.
13. Fast Fourier transform and its applications. Linear and circular convolution. Efficient computation of the convolution sum.
14. Digital signal processor. Fixed-point arithmetic. Signal quantization.
15. Final exam

#### Study Programmes

##### University graduate
Data Science (profile)
Core-elective courses (1. semester)

#### Literature 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 Ruye Wang (2012.), Introduction to Orthogonal Transforms, Cambridge University Press

#### General

ID 223374
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
10 Exercises
20 Laboratory exercises

87 Excellent
75 Very Good
64 Good
51 Acceptable