Skip to content Skip to navigation

OpenStax_CNX

You are here: Home » Content » Encoding Information in the Frequency and Time Domains

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Encoding Information in the Frequency and Time Domains

Module by: Don Johnson. E-mail the author

Summary: This module discusses the Fourier series encoding scheme.

We can create an encoding scheme in the frequency domain to represent an alphabet of letters. But, as this information-encoding scheme stands, we can represent one letter for all time. However, we note that the Fourier coefficients depend only on the signal's characteristics over a single period. We could change the signal's spectrum every T T as each letter is typed. In this way, we turn spectral coefficients on and off as letters are typed, thereby encoding the entire typed document. For the receiver (see the Fundamental Model of Communication) to retrieve the typed letter, it would simply use the Fourier formula for the complex Fourier spectrum for each T T -second interval to determine what each typed letter was. Figure 1 shows such a signal in the time-domain.

Figure 1: The encoding of signals via the Fourier spectrum is shown over three "periods." In this example, only the third and fourth harmonics are used, as shown by the spectral magnitudes corresponding to each T T -second interval plotted below the waveforms. Can you determine the phase of the harmonics from the waveform?
Encoding Signals
Encoding Signals (sig15.png)

In this Fourier-series encoding scheme, we have used the fact that spectral coefficients can be independently specified and that they can be uniquely recovered from the time-domain signal over one "period." Do note that the signal representing the entire document is no longer periodic. By understanding the Fourier series' properties (in particular that coefficients are determined only over a T T -second interval, we can construct a communications system. This approach represents a simplification of how modern modems represent text so that they can be transmitted over telephone lines.

Content actions

Download module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

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