34809 - Biomedical Data and Signals Processing (2nd cycle)

Learning outcomes

Aim of the course is to furnish the fundamental theoretical and practical instruments for the acquisition, numerical processing and classification of signals, with particular emphasis on medical-biological problems. The course treats mono-dimensional time-discrete signals, both deterministic and stochastic in type. It provides the fundamental concepts concerning the design of numerical filters, parameter estimation from signals, the evaluation of power spectral density of a stationary stochastic process, the time-frequency or time-scale methods for the analysis of non-stationary processes, signal classification and its diagnostic use

Course contents

1) Review of biomedical signals. Characteristics and properties: deterministic and stochastic signals, stationarity, ergodicity, spontaneous and induced signals. Signals classification.

2) Main characteristics of discrete time signals. The analog-digital conversion. The discrete time Fourier transform and the Z transform. Characteristics of time invariant systems in the discrete domain: the FIR and IIR systems and their implementation. The discrete time Fourier series and its relationship with the discrete time Fourier transform. Practice exercises: discrete time signals, sampling and frequency analysis.

3) The design of numerical filters. The main design parameters for a filter. Characteristics of IIR filters: Butterworth, Chebyshev and elliptic filters. The design of IIR filters with the impulse invariance method and with the bilinear transform. Characteristics of FIR filters and their design with the window technique. Practical exercises: filtering synthetic and biological signals.

4) Random variables. The fundamental properties of random variables. The joint and conditional probability density function. The covariance matrix. Bayes theorem. Correlation and independence. Practical exercise: probability and correlation.

5) Stochastical processes and power spectral density. Fundamentals of stochastic processes. Classical methods for the estimation of power spectral density: correlogram, periodogram, Welch method. Modern methods for power density estimation: main characteristics of AR, MA and ARMA models. Algorithms for parameter determination in these models: the Yule-Walker equations and Levinson-Durbin recursion. Practical exercises: application of several spectral estimation methods to synthetic and biomedical signals.

6) Non-stationary processes. The time-frequency localisation of a non-stationary signal. The constancy of the product “duration/frequency band”. The short-time Fourier transform and its limitations. Introduction to wavelets and their advantages. The spectrogram. The continuous and the discrete wavelet transforms. The scalogram. The multiresolution analysis and the decomposition of a signal in approximations and details.

7) The statistical pattern recognition. Introduction to machine learning. The Bayes classifiers with minimum error and with minimum risk. Introduction to Support Vector Machines. Empirical evaluation of the error: cross-validation and leave one out. Methods for the estimation of the probability density. ROC analysis: confusion matrix, ROC plane and curves. Practical exercise: ROC analysis.

Readings/Bibliography

Notes provided by the Professor.

A. Oppenheim, R. Schafer. "Discrete-Time Signal Processing", Prentice Hall, 2009.

F. Argenti, L. Mucchi, E. Del Re. “Elaborazione numerica dei segnali”, McGraw-Hill, 2011.

E. Alpaydin. “Introduction to Machine Learning”, Cambridge: The MIT Press, 2009.

B. Boashash, ed.. "Time Frequency Signal Analysis and Processing - A Comprehensive Reference", Elsevier, 2003.

Teaching methods

The course comprehends both ex-cathedra lessons and practical exercises on the personal computer, with the software package matlab. The aim of the lessons is to provide the students with a theoretical knowledge about the main signal processing methods, and to make them aware about the advantages and limitations of each available technique. The practical exercises aim at training the students on the resolution of simple real biomedical problems, and at showing the potential benefits but also the shortcomings and difficulties introduced by processing techniques and software packages.

Assessment methods

Written (including MATLAB exercise in the lab) and oral exam. The Matlab practical exercises carried out during the course must be sent by email 7 days before the written examination. The exam aims at assessing the pursuing of the main objectives:
- knowledge of the main mathematical methods for the analysis of discrete signals;
- knowledge of the main digital filter techniques;
- knowledge of the techniques for the study of stationary and non-stationary stochastic processes;
- knowledge of the methods for statistical classification.
The analytical and synthetic attitudes of the student, and his/her exposition capability are also evaluated during the exam.

Teaching tools

Blackboard, videoprojector.

Notes provided by the Professor.

Personal computer laboratory.

Matlab software package, for performing practical exercise on the informatics laboratory.

Office hours

See the website of Stefano Diciotti