Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Discrete-Time Fourier Transform (DTFT)

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Discrete-Time Fourier Transform (DTFT)

Module by: Richard Baraniuk. E-mail the author

Summary: Details the discrete-time fourier transform.

Note: You are viewing an old version of this document. The latest version is available here.

Discrete-Time Fourier Transform

Xω= n =xne(iωn) X ω n x n ω n
(1)

Inverse Discrete-Time Fourier Transform

xn=12π02πXωeiωnd ω x n 1 2 ω 0 2 X ω ω n
(2)

Relevant Spaces

The Discrete-Time Fourier Transform maps infinite-length, discrete-time signals in l 2 l 2 to finite-length (or 2π 2 -periodic), continuous-frequency signals in L 2 L 2 .

Figure 1: Mapping l 2 Z l 2 in the time domain to L 2 0 2π L 2 0 2 in the frequency domain.
Figure 1 (DTFT1.png)

Content actions

Download module as:

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks