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.
Fausto Ferrari (2014). Fourier TransformEncyclopedia of Thermal Stresses. Dordrecht, Heidelberg, New York, London : Springer Netherlands [10.1007/978-94-007-2739-7_22].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
