Data Analysis and Transformation
1st Cycle Studies
Mathematical Analysis I, Mathematical Analysis II, Linear Algebra and Analytic Geometry, Statistics, Introduction to Programming and Problem Solving, Information Theory.
- 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.
- Slides to support theoretical classes
- Miscellaneous Bibliography
- Practical works
- Quizzes Online (using Moodle) for training and self-learning
- Software: Matlab and Python.
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.
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
- 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.
Alberto Jorge Lebre Cardoso
Mini Tests: 30.0%
- 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