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Statistical Analysis and Signal Processing

Code: M4110     Acronym: M4110     Level: 400

Classification Keyword
OFICIAL Mathematics

Instance: 2020/2021 - 1S Ícone do Moodle

Active? Yes
Web Page: https://moodle.up.pt/course/view.php?id=3583
Responsible unit: Department of Mathematics
Course/CS Responsible: Master's degree in Data Science

Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
M:DS 3 Official Study Plan since 2018_M:DS 1 - 6 42 162

Teaching Staff - Responsibilities

Teacher Responsibility
Ana Paula de Frias Viegas Proença Rocha

Teaching - Hours

Theoretical and practical : 3,00
Type Teacher Classes Hour
Theoretical and practical Totals 1 3,00
Ana Paula de Frias Viegas Proença Rocha 0,00

Teaching language

Suitable for English-speaking students


To provide a current and interdisciplinary perspective of statistical signal analysis and advanced methods of analyzing temporal data and extracting information. Analysis of complex / extensive data by combining predictive methods and data-driven  approaches suitable for Data Science.
To involve the  students in a case study application for the practice and critical perception of the studied methods and underlying software packages and tools used.

Learning outcomes and competences

The student should be able to:

- review essential discrete-time signal processing topics, including sampling effect and transforms

-characterize random signals in time, frequency and time-frequency/scale domain, formulate suitable models, estimate the parameters, and evaluate the quality of the estimates.

-use linear estimation theory, optimal linear estimation, Kalman and Wiener filtering, to solve estimation problems with applications in  signal processing, such as telecommunications, bioengineering and telemedicine, but also in other disciplines such as finance and statistics..

- use adaptive signal processing algorithms for extracting relevant information from noisy signals: emphasis is on recursive, model based estimation methods for time-variant signals and systems and  diverse case studies such as in finance and biomedical applications.

- critically select the methods and software tools for each concrete case study in broad multidisciplinary signal processing contexts with interpretation of the obtained results, by combining signal and data treatment

- Introduction to novel paradigms in statistical signal processing  (selected topics following current interdisciplinary trends, centered in the different student profiles)

Working method


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

Probability and Statistics at introductory level.


Random Processes. Characterization in time and frequency domains. Stationarity and ergodicity. Linear models. Spectral estimation. Parametric and non parametric methods. Introduction to time-frequency/scale analysis and wavelets. Optimal and adaptive signal processing fundamentals. Least mean squares and recursive algorithms.

Introduction to novel paradigms in statistical signal processing.

Applications/illustrations of the methods to case studies.

Mandatory literature

000039792. ISBN: 0-471-59431-8
000089741. ISBN: 0-12-088581-6
000080761. ISBN: 1-58053-610-7

Complementary Bibliography

Steven Lee Brunton; Data-driven science and engineering. ISBN: 978-1-108-42209-3
Trevor Hastie; The elements of statistical learning. ISBN: 978-0-387-84857-0
Semmlow John L.; Biosignal and medical image processing. ISBN: 9781466567368 (Biosignal and medical image processing / John L. Semmlow, Benjamin Griffel)
Vaseghi Saeed V.; Advanced digital signal processing and noise reduction. ISBN: 9780470754061 (Advanced digital signal processing and noise reduction / Saeed V. Vaseghi)
José Luis Rojo Álvarez; Digital signal processing with kernel methods. ISBN: 978-1-118-61179-1 (José Luis Rojo Álvarez;Digital signal processing with kernel methods. ISBN: 978-1-118-61179-1)
Ervin Sejdic, Tiago Falk; Signal processing and machine learning for biomedical big data, Taylor & Francis, 2018. ISBN: 978-1-4987-7345-4

Teaching methods and learning activities

Lectures TP to present and illustrate the topics. Problems / Projects with strong laboratorial computation component using Matlab (R/Python).

A special attention is given to the understanding of the concepts and methods with an effective use of simulated and experimental data. One of the aims of the discipline is also the improvement of the oral and written competences. The discipline presents an important computational component with MATLAB or other adequate computational environment


Matlab ( Toolbox Statistics and Data Mining)
Matlab ( Toolbox Signal Processing)
Matlab ( Toolbox Neural Networks and Deep Learning)


Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Applied mathematics
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation Weight (%)
Prova oral 50,00
Trabalho escrito 50,00
Total: 100,00

Amount of time allocated to each course unit

designation Time (hours)
Elaboração de projeto 25,00
Estudo autónomo 70,00
Frequência das aulas 42,00
Trabalho laboratorial 25,00
Total: 162,00

Eligibility for exams

Minimum of 8 on continous evaluation.
Minimum of 8 in individual project

Calculation formula of final grade

Work / Labs (T-50%) and final Project (P-50%). The final Project evaluation, includes discussion (30%), final presentation (20%) and written report(50%).

Examinations or Special Assignments

Not applicable. Identical for all of the students.

Special assessment (TE, DA, ...)

Not applicable. Identical for all of the students.

Classification improvement

Not applicable for the continous evaluation component T.


This discipline teaching and assessment methods are also adequate for distance learning teaching
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