Politecnico di Torino  
Academic Year 2012/13  
04EQAMA Signal analysis 

1st degree and Bachelorlevel of the Bologna process in Biomedical Engineering  Torino 





Subject fundamentals
The course aims to present the basic knowledge of signal theory and analysis. It provides the fundamental methodological tools for the description and analysis of continuoustime and discretetime, both deterministic and random signals.

Expected learning outcomes
Deterministic, continuoustime signals and systems and their analysis in the frequency domain.
Deterministic, discretetime signals and systems. Basic concepts of probability theory. Continuous and discretetime random signals. Selection and application of appropriate methods for signal analysis. 
Prerequisites / Assumed knowledge
Basic mathematical analysis (integrals, derivatives), linear algebra (vectors, matrices, scalar product, norm).
Indepth knowledge of complex numbers and trigonometry. 
Contents
Definition and classification of signals: continuous / discrete time, deterministic / random
Energy and mean power Fourier Series and Transform LTI systems, impulse response and transfer function Energy spectral density and autocorrelation function Periodic signals and related power spectral density Power spectral density of nonperiodic signals Sampling Theorem Discretetime signals; ztransform, discrete time Fourier transform (DTFT) LTI discretetime systems FIR and IIR filters Introduction to random variables Random processes: definitions Stationary processes: autocorrelation and power spectral density Ergodic processes 
Contents (Prof. M. Visintin)
Classification of signals: continuoustime or discretetime, deterministic or random
Dirac delta Linear time invariant systems: definition, impulse response, convolution (continuous and discrete time) Deterministic and continuoustime systems and signals:  LTI systems: Fourier transform (eigenfunction of convolution), transfer function  Signals: Fourier transform and its properties, evaluation of the main Fourier transforms  Finiteenergy signals: energy, energy spectrum, autocorrelation function  Periodic signals: period and power, Fourier series, Fourier transform, power spectrum, autocorrelation function Sampling theorem Deterministic and discretetime systems and signals:  LTI systems: Z transform and inverse transform, transfer function, poles and zeroes  Signals: Z transform of the main signals  Periodic signals: DFT and IDFT, circular convolution  Use of DFT/IDFT to evaluate the output of an LTI system for a nonperiodic input Relationship between the Fourier transform of a timecontinuous signal and the Z transform of its sampled version. Probability thoery:  Axioms  Conditional probability, Bayes rule, statistical independence  Random variables: probability distribution and density  Couple of random variables: joint probability distribution and density  Mean, mean square value, variance, standard deviation  Gaussian and uniform probability denisty functions and distributions  Central limit theorem Continuoustime random processes:  Examples of random processes  First order probability density function for a random process  Autocorrelation and power spectrum for a stationary and ergodic process  Filtered stationary and ergodic processes  White Gaussian noise 
Delivery modes
The course consists of lectures and exercises. The classroom exercises consist in the solution of exercises related to the program carried out in class.

Texts, readings, handouts and other learning resources
 B. P. Lahti, R. A. Green, Essentials of Digital Signal Processing, Cambridge University Press, 2014
 (alternatively) Lo Presti and F. Neri, The analysis of the signals, CLUT, 1992. In addition, teachers will provide handouts and exercises. 
Test, readings, handouts and other learning resources (Prof. M. Visintin)
L. Lo Presti, F. Neri, 'L'Analisi dei Segnali', CLUT.
L. Lo Presti, F. Neri, 'Introduzione ai processi casuali', CLUT. Soved exercises and exams (download from didattica portal) 
Assessment and grading criteria
Written exam: two exercises, each one encompassing a number of questions, to be carried out in extended form. The exercises will be related to any part of the program, and may also include theoretical questions.

Assessment and grading cirteria (Prof. M. Visintin)
Written exam with theory questions and problems to be solved. Closed book exam (apart from tables of Fourier and Z transforms). Oral exam if requested by the professor.

