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This module gives a brief description of important communication system components: the modulator, the coder/mapper, and the pulse shaper.

The Modulator:

  • Translates “baseband” analog message to “passband”:
    This figure contains two graphs. The first plots f on the horizontal axis and displays a rectangle of height 1 with its base on the horizontal axis and base length from horizontal value -1/2T to 1/2T. There is an arrow to the right of this graph pointing at the second graph, which plots f on the horizontal axis and displays two rectangles. The bases of the rectangles are on the horizontal axis. The midpoint of the base of the left rectangle is at -f_c, and the midpoint of the base of the right rectangle is at f_c. The height of these rectangles is measured as 1/2. There is an arrow pointing both left and right above the arrow to the right, labeled 1/T. This figure contains two graphs. The first plots f on the horizontal axis and displays a rectangle of height 1 with its base on the horizontal axis and base length from horizontal value -1/2T to 1/2T. There is an arrow to the right of this graph pointing at the second graph, which plots f on the horizontal axis and displays two rectangles. The bases of the rectangles are on the horizontal axis. The midpoint of the base of the left rectangle is at -f_c, and the midpoint of the base of the right rectangle is at f_c. The height of these rectangles is measured as 1/2. There is an arrow pointing both left and right above the arrow to the right, labeled 1/T.
    where f c is the “carrier frequency.”
  • There are two principal motivations for doing this:
    1. Often we want to communicate several messages simultaneously (e.g., TV, radio, voice). It's difficult or impossible to dothis if they overlap in frequency!
    2. Wireless EM transmission/reception is much easier at higher frequencies, since need antenna length > λ 10 . ( λ = c f c is wavelength and c =3e8 m/s speed of light.)
      system transmission band λ / 10
      VHF (TV) 30–300 MHz 1–0.1 m
      UHF (TV) 0.3–3 GHz 10–1 cm
      cellular 824–960 MHz 3 cm
      WiFi 2.4 GHz 1 cm
      Notice that practical antenna length determines wheredifferent signal types can be transmitted.

The Coder/Mapper:

  • Coder transforms sequence of message bits into an error-resiliant sequence of coded bits.
  • Mapper transforms coded bits into discrete “symbols.” Ex: If the “symbol alphabet” is { - 3 , - 1 , 1 , 3 } and the symbol mapping is
    bits symbol
    00 3
    01 -1
    10 1
    11 -3
    then ASCII text would be transmitted via
    letter ASCII code symbol sequence
    a 01 10 00 01 -1 1 -3 -1
    b 01 10 00 10 -1 1 -3 1
    c 01 10 00 11 -1 1 -3 3
    d 01 10 01 00 -1 1 -1 -3

Pulse Shaper:

  • Converts symbol sequence into a continuous waveform.
  • In linear modulation schemes, the time- n symbol a [ n ] scales a n T -delayed version of pulse g ( t ) :
    m ( t ) = n a [ n ] g ( t - n T ) "baseband message" T = "symbol period"
    Ex: Say symbol sequence is [ 1 , 3 , - 1 , 1 , 3 ] . Then
    This is a three-part figure of multiple cartesian graphs containing waves. The first is five graphs in a line, aligned with horizontal axes t. In the positive side of the horizontal axis, dashed lines down through the graphs are labeled T, 2T, 3T, 4T, 5T, and 6T. The graphs are labeled from top to bottom, g(t), g(t-T) g(t-2T), g(t-3T), g(t-4T). In the graphs, there is half a small wave, a complete larger wave, and then a second part of a small wave. The peak of the large wave occurs at the horizontal values of 0 in the first, then T, 2T, 3T, and 4T. The second part of this figure plots t on the horizontal axis, and is labeled a[n]g(t - nT) for n = 0, ..., 4. This graph contains five colored curves containing waves of different sizes, each centered at the horizontal axis, and each having different amplitudes. The third part is a graph plotting a horizontal axis t and containing the title y(t) = Σ_n a[n]g(t - nT). This graph contains only one curve, with nonuniform wavelength and varying amplitude, completing three and one half waves. This is a three-part figure of multiple cartesian graphs containing waves. The first is five graphs in a line, aligned with horizontal axes t. In the positive side of the horizontal axis, dashed lines down through the graphs are labeled T, 2T, 3T, 4T, 5T, and 6T. The graphs are labeled from top to bottom, g(t), g(t-T) g(t-2T), g(t-3T), g(t-4T). In the graphs, there is half a small wave, a complete larger wave, and then a second part of a small wave. The peak of the large wave occurs at the horizontal values of 0 in the first, then T, 2T, 3T, and 4T. The second part of this figure plots t on the horizontal axis, and is labeled a[n]g(t - nT) for n = 0, ..., 4. This graph contains five colored curves containing waves of different sizes, each centered at the horizontal axis, and each having different amplitudes. The third part is a graph plotting a horizontal axis t and containing the title y(t) = Σ_n a[n]g(t - nT). This graph contains only one curve, with nonuniform wavelength and varying amplitude, completing three and one half waves.

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Source:  OpenStax, Introduction to analog and digital communications. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col10968/1.2
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