Skip to content Skip to navigation

Connexions

You are here: Home » Content » Signal Sets

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

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

      What is in a lens?

      Lens makers point to Connexions 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 Connexions 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
  • E-mail the author
  • Rate this module (How does the rating system work?)

    Rating system

    Ratings

    Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

    How to rate a module

    Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

    		(0 ratings)

Recently Viewed

This feature requires Javascript to be enabled.

Signal Sets

Module by: Don Johnson

Summary: Introduces binary phase shift keying.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

We represent a bit by associating one of two specific analog signals with the bit's value. Thus, if bn=0 b n 0 , we transmit the signal s 0 t s 0 t ; if bn=1 b n 1 , send s 1 t s 1 t . These two signals comprise the signal set for digital communication and are designed with the channel and bit stream in mind. In virtually every case, these signals have a finite duration TT common to both signals that is known as the bit interval. A commonly used example of a signal set consists of pulses that are negatives of each other.

s 0 t=A p T t s 0 t A p T t (1)
s 1 t=-A p T t s 1 t A p T t (2)

Figure 1
Figure 1 (sig26.png)

Here, we have a baseband signal set suitable for wireline transmission. The entire bit stream bn b n is represented by a sequence of these signals. Mathematically, the transmitted signal has the form

xt=∑n-1bnA p T t−nT x t n n -1 b n A p T t n T (3)
and graphically Figure 2 shows what a typical transmitted signal might be.

Figure 2: The upper plot shows how a baseband signal set for transmitting the bit sequence 0110. The lower one shows an amplitude-modulated variant suitable for wireless channels.
(a)
Figure 2(a) (sig27.png)
(b)
Figure 2(b) (sig29.png)

This way of representing a bit stream—changing the bit changes the sign of the transmitted signal—is known as binary phase shift keying and abbreviated BPSK. Here is an attempt to explain the nomenclature: The word binary is clear enough (one binary-valued quantity is transmitted during a bit interval); changing the sign of sinusoid amounts to changing — shifting — the phase by π (although we don't have a sinusoid yet); and the word "keying" reflects back to the first electrical communication system, also for digital communications: the telegraph.

The datarate RR of a digital communication system is how frequently an information bit is transmitted. In this example it equals the reciprocal of the bit interval: R=1T R 1 T . Thus, for a 1 Mbps (megabit per second) transmission, we must have T=1μs T 1 μs .

Comments, questions, feedback, criticisms?

Send feedback