Lecturer: Giuseppe Savarè  

Course name: Modelli e metodi matematici II
Course code: 064072
Degree course: Ingegneria Elettronica
Disciplinary field of science: MAT/05
L'insegnamento costituisce attività di base per: Ingegneria Elettronica e delle Telecomunicazioni
University credits: CFU 5
Course website: http://www.imati.cnr.it/~savare/didattica/modelli/index
.html

Specific course objectives

Learn basic facts of Distribution theory with applications to signals: derivatives, convolutions, filters, Fourier, Laplace and Zeta transforms, samplings.

Course programme

Distributions and applications to signal theory

• Introduction, impulse, definition and examples.
• Basic operations on distributions
• Convergence and series of distributions
• Tempered distributions, Fourier transform
• The Fourier transform of a periodic signal, the link with Fourier series
• Convolutions and filters, fundamental solution of differential equations
• Discrete signals and Zeta transform
• Sampling and reconstruction, Shannon theorem, DFT.

Course entry requirements

All the mathematical notions developed in the first three years of degree.

Course structure and teaching

Lectures (hours/year in lecture theatre): 30
Practical class (hours/year in lecture theatre): 15
Practicals / Workshops (hours/year in lecture theatre): 0
Project work (hours/year in lecture theatre): 0

Suggested reading materials

C. Gasquet, P. Witomski. Fourier Analysis and Applications. Filtering, Numerical Computation, Wavelets. Springer, New York, 1999.

P. Bremaud. Mathematical principles of signal processing: Fourier and wavelet analysis. Springer, New York, 2002.

E. Roubine. Distributions Signal. Ed. Eyrolles, Paris, 1982.

G. Gilardi. Analisi Tre. Mc Graw Hill, Milano, 1994.

Testing and exams

Oral examination.