Skip to content Skip to navigation


You are here: Home » Content » Sampling CT Signals: A Frequency Domain Perspective


Recently Viewed

This feature requires Javascript to be enabled.


(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Sampling CT Signals: A Frequency Domain Perspective

Module by: Robert Nowak. E-mail the author

Summary: The module will provide an introduction to sampling a signal in the frequency domain and go through a basic example.

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

Understanding Sampling in the Frequency Domain

We want to relate x c t x c t directly to xn x n . Compute the CTFT of x s t= n = x c nTδtnT x s t n x c n T δ t n T

X s Ω= n = x c nTδtnTe(i)Ωtd t = n = x c nTδtnTe(i)Ωtd t = n =xne(i)ΩnT= n =xne(i)ωn=Xω X s Ω t n x c n T δ t n T Ω t n x c n T t δ t n T Ω t n x n Ω n T n x n ω n X ω
where ωΩT ω Ω T and Xω X ω is the DTFT of xn x n .


X s Ω=1T k = X c Ωk Ω s X s Ω 1 T k X c Ω k Ω s
Xω=1T k = X c Ωk Ω s =1T k = X c ω2πkT X ω 1 T k X c Ω k Ω s 1 T k X c ω 2 k T
where this last part is 2π 2 -periodic.


Figure 1
Figure 1 (sec10_fig1.png)

Example 1: Speech

Speech is intelligible if bandlimited by a CT lowpass filter to the band ±4 kHz. We can sample speech as slowly as _____?

Figure 2
Figure 2 (sec10_fig2.png)
Figure 3: Note that there is no mention of TT or Ω s Ω s !
Figure 3 (sec10_fig3.png)

Relating x[n] to sampled x(t)

Recall the following equality: x s t= n nxnTδtnT x s t n n x n T δ t n T

Figure 4
Figure 4 (sec10_fig4.png)

Recall the CTFT relation:

xαt1αXΩα x α t 1 α X Ω α
where αα is a scaling of time and 1α 1 α is a scaling in frequency.
X s ΩXΩT X s Ω X Ω T

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


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