0.1 Preview of comm system components

The Modulator:

• Translates “baseband” analog message to “passband”:

  

  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 $>\frac{\lambda }{10}$ . ( $\lambda =\frac{c}{f_c}$ is wavelength and c =3e8 m/s speed of light.)

     system	transmission band	$\lambda /10$
     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 $a\left[n\right]$ scales a $nT$ -delayed version of pulse $g\left(t\right)$ :
  $$\begin{array}{ccc}\hfill m\left(t\right)& =& \sum _{n}a\left[n\right]g(t-nT)\text{"baseband message"}\hfill \\ \hfill T& =& \text{"symbol period"}\hfill \end{array}$$
  Ex: Say symbol sequence is $[1,3,-1,1,3]$ . Then