Fundamentals of Signal Processing

Code:

L.EEC025

Acronym:

FPS

Keywords
Classification	Keyword
OFICIAL	Basic Sciences for Electrotechnology

Instance: 2025/2026 - 1S

Active?	Yes
Web Page:	https://moodle2526.up.pt/course/view.php?id=5115
Responsible unit:	Department of Electrical and Computer Engineering
Course/CS Responsible:	Bachelor in Electrical and Computer Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EEC	243	Syllabus	3	-	6	52	162

Teaching language

Portuguese and english

Objectives

This course aims to motivate students to the fundamental concepts, techniques and tools of analysis and design in the field of Signal Processing (SP). A particular emphasis is given to specific topics, notably sampling and reconstruction of signals; the Z-Transform; the design and realization of FIR and IIR filters; the Discrete Fourier Transform (DFT) and its fast computation through the FFT; practical applications of the DFT mainly in correlation studies and spectral analysis; introduction to linear adaptive filtering. A central objective is to empower students to solve signal processing-related problems and to motivate them to laboratory experimentation through the design, testing, and practical validation of solutions to selected challenges by following a "hands-on", "learning-by-doing", and "active learning" approach.

Learning outcomes and competences

Attendance and successful completion of this course will enable students

-to understand the process of sampling and signal reconstruction and to anticipate its implications when applied to real-world signals;

-to design, implement, and test digital FIR and IIR filters according to specific operation and signal conditioning requirements, including in adaptive filtering;

-to fully understand the DFT, its circular properties, and fast implementation alternatives (FFT);

-to be able to identify and realize potential applications of the DFT, particularly in fast FIR filtering, correlation studies, and spectral analysis.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Signals and Systems (L.EEC015), or equivalent

Program

1. Characterization and representation of discrete-time signals and systems. Discrete-time deterministic and random signals.
2. The discrete-time Fourier Transform. Properties and transform pairs.
3. Sampling and reconstruction of signals. The sampling theorem and aliasing. Discrete-time processing of continuous-time signals.
4. The Z-Transform and its properties. Characterization in the Z domain of FIR and IIR discrete-time systems.
5. Inverse systems, all-pass systems, minimum-phase, and maximum-phase systems. FIR linear-phase systems.
6. Design of discrete-time IIR and FIR filters and their realization structures
7. Introduction to linear adaptive filtering.
8. The Discrete Fourier Transform (DFT) and its periodic properties.
9. The computation of the DFT using the Fast Fourier Transform (FFT).
10. Application of the FFT in FIR fast-convolution, in correlation studies, and in spectral estimation.

Mandatory literature

Alan V. Oppenheim; Discrete-time signal processing. ISBN: 0-13-083443-2

Complementary Bibliography

Sanjit K. Mitra; Digital signal processing. ISBN: 0-07-122607-9
John G. Proakis; Digital signal processing. ISBN: 0-13-187374-1

Teaching methods and learning activities

The teaching methodology is based on lectures -T (2h/week) and laboratory classes -PL (2h/week).

Lectures are not intended for the classical presentation of the course topics, with students having a passive role. Instead, they assume an "active learning" attitude on the part of the students, given that, whenever possible, these classes will adopt the "flipped classroom" principle, according to which the theory presentation of the course topics will be made available on video for viewing outside the classes.

The focus of lectures will therefore be i) to summarize the theory related to the course topics and, whenever appropriate, illustrate its application, ii) to introduce the themes of laboratory assignments as well as problems illustrating the application of the theoretical concepts, and iii) to create a space, at the end of each lecture, for consolidation and assessment of understanding and knowledge, via Wooclap/Moodle, with an impact of 15% on the distributed assessment (Active Lectures-AL).

Laboratory classes include two components, one of which impacts distributed assessment (DA): i) discussion of conventional or Matlab-based problem-solving, by the teacher or students from a peer-to-peer learning/teaching perspective (component with no contribution to DA); and ii) laboratory work in groups of four students using a real-time digital signal processing platform. At the end of each class, there is an individual micro-test that aims to test understanding and knowledge related to the laboratory work and/or topics studied in the most recent lectures (component weighted at 85% in DA).

Software

Matlab

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Participação presencial	7,50
Exame	50,00
Trabalho laboratorial	42,50
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	84,00
Frequência das aulas	52,00
Trabalho laboratorial	26,00
Trabalho de campo
Total:	162,00

Eligibility for exams

Participating in the activities of active lectures and PL classes is key to obtaining the distributed assessment grade, which, in turn, is essential for admission to the final exam.

The distributed assessment (AD) grade is awarded to students who do not exceed the absence limit (according to the FEUP General Assessment Regulation) and have taken the online and/or paper micro-tests (quizzes), provided for both active lectures (Active Lectures - AL), and laboratory classes (PL), in addition to preparing and performing the proposed laboratory work.

All quizzes are individual, although laboratory work is carried out in groups of 4 students.

The individual online quizzes taken via Wooclap/Moodle at the end of each active lecture represent 15% of the AD (AL component). The individual paper micro-tests taken at the end of each laboratory class represent 85% of the AD (PL component).

AD = 0.85×PL + 0.15×AL

Approval is conditional upon obtaining at least a 10.0 (ten points and zero tenths) on the distributed assessment.

Calculation formula of final grade

The final exam consists of a written exam lasting 2 hours. This exam is closed book but a formulae sheet will be provided.

The final grade (C) is obtained by combining the distributed assessment score (AD>=10.0) , and the score of the written exam (E> = 7.0) using the formula:

C = 0.5×AD + 0.5×E.

 

The final grade is conditional on a minimum score of 7.0 (seven points and zero tenths) in the written exam, and a minimum score of 10.0 points in the AD component.

All scores/grades presume the [0, 20] range.

Special assessment (TE, DA, ...)

No student enrolled in the course is exempt from participating in the various distributed assessment components. If, due to justified and force majeure reasons, a student benefiting from a special status is not able to participate in those components, he/she is subject to the development of a mandatory project based on the signal processing platform adopted in laboratory classes and whose theme and realization objectives must be agreed upon with the principal instructor of the course. This project must be documented through a report, and its operation must be demonstrated through a practical laboratory exam.

Classification improvement

Due to the fact that the distributed assessment score (AD) is based on several components evaluated in different types of classes and throughout the semester, the participation score is not subject to improvement through any modality replacing it at the end of the semester. As a consequence, only the final exam score (E) can be improved according to the current rules.