dc.contributor.advisor |
Roy, Tristan |
dc.contributor.author |
Fneich, Fatima |
dc.date.accessioned |
2023-08-18T04:46:56Z |
dc.date.available |
2023-08-18T04:46:56Z |
dc.date.issued |
2023-08-18 |
dc.date.submitted |
2023-08-17 |
dc.identifier.uri |
http://hdl.handle.net/10938/24119 |
dc.description.abstract |
The goal of this thesis is to study signals that have a regularity property defined in
the frequency space, such as a decay on average of the amplitude of their Fourier
transform, by using techniques from frequency analysis. Frequency analysis is a set
of techniques that involve an analysis in the Fourier domain. We review some of
these techniques and some principles. More precisely we will decompose a signal into
countable sums of functions of which the Fourier transform is compactly supported in
a ball or an annulus by performing a Littlewood–Paley decomposition. We will apply
this technique to study the properties of functions having a specific regularity. Over
two hundred years ago, Fourier studied problems related to the series expansions
of periodic signals using elementary trigonometric polynomials. The theory was
extended to non-periodic signals by using the Fourier transform and forms the core
of harmonic analysis. Harmonic analysis is used in various fields such as signal
processing and partial differential equations (PDEs). |
dc.language.iso |
en |
dc.subject |
Mathematics |
dc.title |
Frequency Analysis and Applications |
dc.type |
Thesis |
dc.contributor.department |
Department of Mathematics |
dc.contributor.faculty |
Faculty of Arts and Sciences |
dc.contributor.commembers |
Shayya, Bassam |
dc.contributor.commembers |
Bertrand, Florian |
dc.contributor.degree |
MS |
dc.contributor.AUBidnumber |
202221546 |