Abstract
In Chapter 2 the basic definitions of Fourier transforms were introduced along with sufficient conditions for the transforms to exist. In this chapter we extend the Fourier transform definitions to include some important signals violating the sufficient conditions seen thus far. We shall see that in some cases the extension is straightforward and simply replaces the basic definitions by a limiting form. In other cases the definitions cannot be patched up so easily and we need to introduce more general ideas of functions or signals in order to construct useful Fourier transform pairs. The emphasis in this chapter is on continuous time, since that is where most of the difficulties arise.
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 Science+Business Media New York
About this chapter
Cite this chapter
Gray, R.M., Goodman, J.W. (1995). Generalized Transforms and Functions. In: Fourier Transforms. The Springer International Series in Engineering and Computer Science, vol 322. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2359-8_5
Download citation
DOI: https://doi.org/10.1007/978-1-4615-2359-8_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-6001-8
Online ISBN: 978-1-4615-2359-8
eBook Packages: Springer Book Archive