Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T08:40:18.670Z Has data issue: false hasContentIssue false

13 - Trigonometric Interpolation and the Fast Fourier Transform

from Part II - Constructive Approximation Theory

Published online by Cambridge University Press:  29 September 2022

Abner J. Salgado  and
Steven M. Wise
Abner J. Salgado
Affiliation:
University of Tennessee, Knoxville
Steven M. Wise
Affiliation:
University of Tennessee, Knoxville
Get access

Summary

This chapter begins with the study of trigonometric interpolation and the discrete Fourier transform. As a first application, the numerical integration of periodic functions is discussed. More detailed topics, like existence and uniqueness of trigonometric interpolants, as well as alias as convergence of trigonometric interpolation are discussed. An important practical tool, the fast Fourier transform (FFT) is then introduced. With this at hand the most rudimentary ideas of signal processing are presented.

Keywords

Trigonometric interpolationintergration of periodic functionsthe finite Fourier transformthe FTTFourier matricestrigonometric least squares approximation
Type
Chapter
Information
Classical Numerical Analysis
A Comprehensive Course
 , pp. 345 - 371
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×