Data Analysis and Transformation

Recommended Prerequisites

Mathematical Analysis I, Mathematical Analysis II, Linear Algebra and Analytic Geometry, Statistics, Introduction to Programming and Problem Solving, Information Theory.

Teaching Methods

- Theoretical classes (2h/week) for presentation and discussion of the matter and problem solving, establishing links with the other classes, using slides and computer demonstrations.

- Theoretical-practical classes (1h/week) for introduction to analytical and computational resolution of practical exercises.

- Practical Laboratorial classes (2h/week) to support the execution of several practical works.

 

Resources:

- Slides to support theoretical classes

- Miscellaneous Bibliography

- Practical works

- Quizzes Online (using Moodle) for training and self-learning

- Software: Matlab and Python.

Learning Outcomes

This course corresponds to a broad and integrated vision of the tools of data analysis, modelling and transformation for the computational treatment of the dynamic phenomena and processes of the material and immaterial worlds. This is covered in specific contexts of Informatics Engineering and of its interconnection with other domains

 The course aims to develop the following skills:

-Understanding and interpretation of dynamic phenomena and processes of the real and virtual worlds

-Ability for data analysis supported by computational tools

-Deepening of mathematical reasoning to information extraction

-Ability to solve practical problems supported on the analysis and transformation of one and multi-dimensional data in time, space and frequency domains

The course also contributes to the development of skills at the level of teamwork, critical thinking, argumentative capacity, research and self learning.

Work Placement(s)

No

Syllabus

Chapter 1: Introduction:

- Reasons for Data Analysis and Transformation

- Analysis of dynamic phenomena

- Environment-computer interaction

- Signals and their properties

 

Chapter 2: Time Series Analysis

- Introduction

- Stationary processes

- Non-stationary processes

- Components of the Time Series

- Models identification

 

Chapter 3: Linear Systems

- Discrete-Time Systems

- Z Transform

- Properties of systems

- Systems Analysis

 

Chapter 4: Fourier Transforms

- Fourier Transforms (FS, FT, DTFT, DFT)

- Frequency response and sampling theorem

- Resolution and Noise

- Digital filters

 

Chapter 5: Time-Frequency Analysis

- Short-Time Fourier Transform (STFT)

- The dilemma of the uncertainty principle

- Wavelet Transform

 

Chapter 6: Other Transforms

- Karhunen-Loéve Transform

- Other transforms of orthogonal basis

- Transformations for data compression

- Examples in various application domains.

Head Lecturer(s)

Alberto Jorge Lebre Cardoso

Assessment Methods

Assessment
Project: 15.0%
Mini Tests: 30.0%
Exam: 55.0%

Bibliography

- Steven Smith, “The Scientist and Engineer’s Guide to Digital Signal Processing”, eBook: http://www.dspguide.com/

- Glyn James, "Advance Modern Engineering Mathematics", 4th edition, Pearson, 2011

- A. V. Oppenheim, R. W. Shafer, “Discrete-time signal processing”, 2nd ed. Prentice-Hall, 1999

- K. Sayood, “Introduction to data compression”, 2nd edition, Morgan Kaufman, 2000

- J. Stein, “Digital Signal Processing – a computer science perspective”, Wiley, 2000

- E. Kamen, B. Heck, “Fundamentals of Signals and Systems - Using Matlab”, Prentice Hall, 1997

- Chatfield, C., “The analysis of time series – an introduction”. 5th ed. Chapman and Hall, London, UK, 1996

- Brockwell and Davis, Introduction to Time Series and Forecasting, Second Edition, Springer, 2003