1. Physically short channels can use digital signals.
   1. Simpler for digital equipment to send and receive.
   2. Used inside the box.
   3. Used for short distance connections, like USB.
2. When you don't want to use a digital signal.
   1. Over distance, digital signals spread out and lose their sharp edges.
      
   2. Sinusoidal signals travel much better.
   3. Radio signals are already sinusoidal. Nature rarely makes sharp corners.
3. Modulation
   1. Send information by manipulating a carrier.
   2. A carrier is a sine wave of some chosen shape.
   3. A data signal is used to manipulate the carrier. Can manipulate any combination of
      1. Amplitude
      2. Frequency
      3. Phase
   4. Examples
      1. Analog Modulation.
      2. Digital Modulation (or keying).
      3. Combinations.
      4. Example drawings are exaggerated.
         1. Signals usually must reside within a narrow channel (range of frequencies), so frequency shifts must be small.
         2. Amplitude must stay large enough for easy detection, so only small reductions from the maximum are in order.
   5. Frequency and phase are not usually combined. Difficult for the receiver to distinguish.
4. Constellation Diagrams.
   1. A way to represent a modulation using frequency and phase.
   2. The phase is represented by the radial distance from the positive x axis.
   3. The amplitude is the linear distance from the origin.

      1 amp, 2 phases	1 amp, 4 phases	2 amps, 2 phases	2 amps, 12 phases (16 of 24 combos used)

5. Modems.
   1. Modem is a contraction of “modulator-demodulator”.
   2. Occasionally devices are made separately, but almost never.
   3. So the modulator and demodulator are in the same box, called a modem.
   4. Modems are needed for long wired connections, optical connections, and radio (including WiFi).
   5. Modems may be called something else.
6. Dial-up Modems.
   1. Dial-up modems are a hack to deal with the situation at the end of the 20th century.
   2. You would like to have lots of digital connections to carry Internet traffic to pretty much every home and business. You don't.
   3. Creating them takes much time and money.
   4. You do have lots of telephone landlines designed to carry an analog voice signal.
   5. The voice channel does not have much bandwidth:
   6. The range of usable frequencies, 600-3000, gives 2400 Hz bandwidth.
   7. Fancy coding schemes help a lot.

      V.32, 32 combos 9600bps	V.32bis, 128 combos 14,400bps