Digital Signal Processing

Data is displayed for the academic year: 2025./2026.

Lecturers

Assoc. Prof.
Tomislav Petković
PhD
Prof.
Davor Petrinović
PhD

Laboratory exercises

Assoc. Prof.
Juraj Petrović
PhD

Course Description

Digital signal processing is the use of computers and of specialized processors for digital signal processing with the purpose of improving signal properties, which is usually achieved by filtration.
In this course the student will acquire fundamental theoretical knowledge of digital signal processing and will study the basic concepts of signal representation and of signal filtering.
The following topics are covered: Time discrete signals and systems. Representation of signals and systems in transform domain (Fourier, Laplace and Z transforms). Signal decomposition. Signal sampling and reconstruction. The sampling theorem. Spectral analysis of signals, DFT and FFT. Invertible systems and deconvolution. Types of linear time-invariant systems. Phase and group delay. Linear phase systems. Filtering. Selective filters. All-pass filters. Minimum phase filters. Phase correctors. Classical design of digital filters. Computer-aided design of optimal digital filters. Implementation of digital filters. Digital biquad section. Filter structures. Number representation and overflow. Dynamic range scaling. Quantization of filter coefficients. Finite world-length effects. Digital signal processors. Multirate digital signal processing. Decimation and interpolation. Filter banks.

Prerequisites

A good background in signal processing including discrete-time systems, Fourier transform, and Z transform. A goot backgorund in mathematics including linear algebra, vector spaces, calculus and complex analysis is also assumed.

Study Programmes

University graduate
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Learning Outcomes

  1. Define the basic concepts of digital signal processing
  2. State and explain the sampling theorem
  3. Apply the fast Fourier transform as a signal analysis and processing tool
  4. Identify a filter type and determine its frequency response
  5. Compare digital filter structures
  6. Select which digital filter to use depending on the application and the specification
  7. Design an optimal digital filter using a computer
  8. Analyze and implement time-discrete and digital system using block diagrams and signal-flow graphs
  9. Combine basic blocks of multirate systems to realize a multirate filter bank

Forms of Teaching

Lectures

Lectures present theoretical concepts.

Exercises

Recitations include solving practical tasks and discussing solving procedures.

Laboratory

Laboratory exercises introduce students to digital signal processing hardware.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 50 % 20 % 50 % 20 %
Homeworks 100 % 0 % 100 % 0 %
Quizzes 0 % 10 % 0 % 10 %
Mid Term Exam: Written 0 % 25 % 0 %
Final Exam: Written 0 % 25 %
Final Exam: Oral 20 %
Exam: Written 50 % 50 %
Exam: Oral 20 %
Comment:

The prerequisite for taking any written exam is the submission of handwritten solutions for all homework assignments covering the relevant exam; specifically, about first half of the assignments is the requirement for the midterm exam, the rest is the requirement for the final exam, and all are required for the comprehensive exams.
Mandatory prerequisites for the oral exam include achieving at least 50% on the written exams (either the midterm and final exam combined, or the comprehensive exam) and at least 50% on the laboratory exercises.
A minimum of 4 points is required to pass the oral exam.

Week by Week Schedule

  1. Introduction. Review: time discrete signals and systems; Fourier transforms (DFT, DTFT and CTFT).
  2. Review: representation of signals and systems in transform domain (Fourier, Laplace and Z transforms).
  3. Signal decomposition. Signal sampling and reconstruction. The sampling theorem. Spectral analysis. DFT and FFT.
  4. Convolution and deconvolution. Invertible systems. Minimum phase systems. Relation between amplitude and phase response for minimum phase systems.
  5. Interpretation of magnitude and phase responses. Phase delay. Group delay. Phase distortions. Linear phase systems. Negative group delay.
  6. Relation between time-continuous and time-discrete systems. Euler transform. Bilinear transform.
  7. Filtration. Digital filter specification. Filter types: selective filters; all-pass filters; minimum phase filters; and phase correctors.
  8. Midterm exam
  9. FIR filter design: window method; least-squares design; Parks-McClellan FIR filter design.
  10. IIR filter design: impulse invariance method; bilinear transform; Yule-Walker IIR filter design.
  11. Implementation of digital filters. Digital biquad section. Filter structures.
  12. Number representation and overflow. Dynamic range scaling. Quantization of filter coefficients. Finite world-length effects. Digital signal processors.
  13. Multirate digital signal processing. Decimation and interpolation. Filter banks.
  14. Fast Fourier transform. Efficient computation of convolution and of correlation between finite duration signals.
  15. Final exam

Literature

Sanjit Kumar Mitra (2010.), Digital Signal Processing, McGraw-Hill
Alan V. Oppenheim, Ronald W. Schafer (2011.), Discrete-time Signal Processing, Prentice Hall
John G. Proakis, Dimitris G. Manolakis (2006.), Digital Signal Processing, Pearson
Paolo Prandoni, Martin Vetterli (2008.), Signal Processing for Communications, EPFL Press

General

ID 222528
  Winter semester
5 ECTS
L1 e-Learning
45 Lectures
0 Seminar
10 Exercises
20 Laboratory exercises
0 Project laboratory
0 Physical education excercises

Grading System

87 Excellent
75 Very Good
64 Good
51 Sufficient

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