Statistical Analysis and Signal Processing

Code:

M4110

Acronym:

M4110

Level:

400

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2019/2020 - 1S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2602#section-0
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master 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	6	Official Study Plan since 2018_M:DS	1	-	6	42	162

Teaching language

Suitable for English-speaking students

Objectives

To provide knowledge for the analysis and digital processing of stochastic signals, approaching in a global way the modeling, the spectral estimation and the optimal and adaptive filtering.

Namely,

Provide the students with a general perspective of the main statistical signal analysis methods for data analysis and noise reduction (exploratory data analysis and visualization; data preprocessing, spectral analysis and filtering; model based / datadriven methods and its evaluation).
Develop the students awareness of the richness and versatility of modern statistical signal processing  in the present computer age, as a tool for analysis of the data temporal structure and information extraction. Critical mastering of the underlying methods and tools.
Engage the students in a case study application for practice and critical insight of the studied methods.

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 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)

Working method

Presencial

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

Probability and Statistics at introductory level.

Program

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

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
Trevor Hastie; The elements of statistical learning. ISBN: 978-0-387-84857-0

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

Software

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

keywords

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.