Skip to content Skip to navigation Skip to collection information

Connexions

You are here: Home » Content » Fundamentals of Signal Processing » Systems View of Sampling and Reconstruction

Navigation

Table of Contents

Lenses

What is a lens?

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.

This content is ...

In these lenses

  • SigProc display tagshide tags

    This collection is included inLens: Signal Processing
    By: Daniel McKenna

    Click the "SigProc" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

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

Systems View of Sampling and Reconstruction

Module by: Anders Gjendemsjø. E-mail the author

Summary: An overview of sampling and reconstruction on a system level.

Ideal reconstruction system

Figure 1 shows the ideal reconstruction system based on the results of the Sampling theorem proof.

Figure 1 consists of a sampling device which produces a time-discrete sequence xs⁢nxsn. The reconstruction filter, h⁢tht, is an ideal analog sinc filter, with h⁢t=sinc⁢tTs h t sinc t Ts . We can't apply the time-discrete sequence xs⁢nxsn directly to the analog filter h⁢tht. To solve this problem we turn the sequence into an analog signal using delta functions. Thus we write xs⁢t=∑n=−∞∞xs⁢n⁢δ⁢t−n⁢T xs t n xs n δ t n T .

Figure 1: Ideal reconstruction system
Figure 1 (ideal.jpg)
But when will the system produce an output x̂⁢t=x⁢t x̂ t x t ? According to the sampling theorem we have x̂⁢t=x⁢t x̂ t x t when the sampling frequency, FsFs, is at least twice the highest frequency component of x⁢txt.

Ideal system including anti-aliasing

To be sure that the reconstructed signal is free of aliasing it is customary to apply a lowpass filter, an anti-aliasing filter, before sampling as shown in Figure 2.

Figure 2: Ideal reconstruction system with anti-aliasing filter
Figure 2 (sampling_antialias.jpg)
Again we ask the question of when the system will produce an output x̂⁢t=s⁢t x̂ t s t ? If the signal is entirely confined within the passband of the lowpass filter we will get perfect reconstruction if FsFs is high enough.

But if the anti-aliasing filter removes the "higher" frequencies, (which in fact is the job of the anti-aliasing filter), we will never be able to exactly reconstruct the original signal, s⁢tst. If we sample fast enough we can reconstruct x⁢txt, which in most cases is satisfying.

The reconstructed signal, x̂⁢t x̂ t , will not have aliased frequencies. This is essential for further use of the signal.

Reconstruction with hold operation

To make our reconstruction system realizable there are many things to look into. Among them are the fact that any practical reconstruction system must input finite length pulses into the reconstruction filter. This can be accomplished by the hold operation. To alleviate the distortion caused by the hold opeator we apply the output from the hold device to a compensator. The compensation can be as accurate as we wish, this is cost and application consideration.

Figure 3: More practical reconstruction system with a hold component
Figure 3 (sampling_hold.jpg)
By the use of the hold component the reconstruction will not be exact, but as mentioned above we can get as close as we want.

Collection Navigation

Content actions

Download module as:

PDF | More downloads ...

Add:

Collection 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

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