# FOURIER ANALYSIS

iten
Code
61682
2017/2018
CREDITS
8 credits during the 1st year of 9011 Mathematics (LM-40) GENOVA
SCIENTIFIC DISCIPLINARY SECTOR
MAT/05
LANGUAGE
Italian
TEACHING LOCATION
GENOVA (Mathematics)
semester
1° Semester
Teaching materials

## OVERVIEW

Language: Italian

## AIMS AND CONTENT

LEARNING OUTCOMES

The aim of the course is to provide an introduction to the ideas and methods of Fourier's analysis, the bull, the straight and the discrete case. Among the applications considered, particular emphasis will be placed on problems and techniques of signal analysis, such as the sampling theorem and the transformation of Gabor.

TEACHING METHODS

Teaching style: In presence

SYLLABUS/CONTENT

PROGRAM :

Fourier series. The space of periodic square summable functions. Orthorormal basis. Fourier series. Gibbs phenomenon. Fourier transform of periodic absolute integrable functions. Applications: spectral methods for partial differential equations.

Fourier integrals Fourier integral of absolute integrable functions on R. Fourier transform of elementary fiunzions. Convolution. Approximate indentities. Inversion formula. Fourier transform of square integrable functions. Poisson summation formula. The Paley-Wiener theorem.  Discrete Fourier transform. Fast Fourier Transform. Cosine transform.

Signal analysis. Shannon theorem. Hilbert transform. Gabor transform

SUGGESTED  BOOKS:

V. Del Prete Introduzione all'analisi di Fourier Dispense on line.

Y. Katznelson An introduction to harmonic analysis Collocaz Bibl. DIMA 43-1968-07.

E. O. Brigham, The Fast Fourier Transform, Prentice Hall Englewood Cliffs, Boston,1974. -

H. Dym - H. P. Mc Kean, Fourier Series and Integrals, Academic Press, 1972.

I. Korner, Fourier Analysis, 1995.  - I. Korner, Exercises for Fourier Analysis, 1995.
E. Prestini, Applicazioni dell'analisi armonica. U.Hoepli,Milano, 1996I.

E. Prestini, The Evolution of Applied Harmonic Analysis. Models of the Real World Series, A Birkhäuser 2004.

G.B. Folland,  Fourier analysis and its applications Collocaz Bibl. DIMA 42-1992-01.  The examination os oral

## TEACHERS AND EXAM BOARD

Exam Board

FILIPPO DE MARI CASARETO DAL VERME (President)

ERNESTO DE VITO

GIANCARLO MAUCERI

## LESSONS

TEACHING METHODS

Teaching style: In presence

LESSONS START

The class will start according to the academic calendar.

Class schedule

FOURIER ANALYSIS

## EXAMS

EXAM DESCRIPTION

Oral.

Exam schedule

Date Time Location Type Notes
17/01/2018 14:30 GENOVA Orale
31/01/2018 09:30 GENOVA Orale
13/02/2018 09:30 GENOVA Orale
06/06/2018 09:30 GENOVA Orale
19/06/2018 09:30 GENOVA Orale
11/07/2018 09:30 GENOVA Orale
12/09/2018 09:30 GENOVA Orale