Let's just dive right in. We'll use a signal that is transmitting at 3600 bps, or 3 bits per baud. This means that we can represent 8 binary combinations.

We'll use 2 measures of amplitude, 1 and 2, just we did before. We'll also use 4 possible phase shifts, like we did before. Combining the two, we have 8 possible waves that we can send. How convenient. :)

First step is to generate a table to show us which waves correspond to which binary combination. This can basically be done at random, although modem manufacturers have agreed on standards.

Bit value |
Amplitude |
Phase shift |

000 | 1 | None |

001 | 2 | None |

010 | 1 | 1/4 |

011 | 2 | 1/4 |

100 | 1 | 1/2 |

101 | 2 | 1/2 |

110 | 1 | 3/4 |

111 | 2 | 3/4 |

Let's encode a big bit stream:

First, we break it up into 3-bit triads:

Now all we have to do is figure out what the resulting signal
should look like. Remember that we shift each wave *relative
to the wave before it*!

(These values *are* correct.)

This is the technique most often used. You can imagine how many different amplitudes and phase shifts are needed for 28.8 kbps, which uses 24 bits per baud!