Abstract
Fourier analysis can be illustrated by analogies from optics. Given a light beam, the goal of spectral analysis is to determine the monochromatic beams it contains; that is, the beams of the form exp\(\left( {\frac{{2i\pi }}{\lambda }t} \right)\). Once a spectral analysis has been carried out, one can ask whether the analysis is exhaustive: is all the energy of the beam really concentrated in the band of frequencies where the spectral analysis was done? One can also ask whether the beam can be reconstructed from its monochromatic components: can spectral synthesis be performed?
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer-Verlag New York, Inc.
About this chapter
Cite this chapter
Malliavin, P. (1995). Fourier Analysis. In: Integration and Probability. Graduate Texts in Mathematics, vol 157. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4202-4_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4202-4_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8694-3
Online ISBN: 978-1-4612-4202-4
eBook Packages: Springer Book Archive