The Fourier transform is a key tool in several research fields: engineering, mathematics, applied mathematics, and physical science. We approach to this instrument assuming that the mathematical background of the readers might be various. Hence, the subject has been developed progressively. In particular in the first vintroductory part, the main relationship with the Fourier series has been put in evidence. Successively a rigorous mathematical discussion permits to deal with the subject in different functional spaces even arriving to the distributional framework. Some examples and applications are vintroduced and developed in the detail. In order to give the larger spectrum concerning the Fourier transform applications, even some topics like the discrete Fourier transform and the Shannon theorem are discussed.

Fourier TransformEncyclopedia of Thermal Stresses

FERRARI, FAUSTO
2014

Abstract

The Fourier transform is a key tool in several research fields: engineering, mathematics, applied mathematics, and physical science. We approach to this instrument assuming that the mathematical background of the readers might be various. Hence, the subject has been developed progressively. In particular in the first vintroductory part, the main relationship with the Fourier series has been put in evidence. Successively a rigorous mathematical discussion permits to deal with the subject in different functional spaces even arriving to the distributional framework. Some examples and applications are vintroduced and developed in the detail. In order to give the larger spectrum concerning the Fourier transform applications, even some topics like the discrete Fourier transform and the Shannon theorem are discussed.
2014
Encyclopedia of Thermal Stresses
1742
1769
Fausto Ferrari
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/301918
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact