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1. Don Romano (alt) (thor@noagendasocial.com)'s status on Sunday, 21-Apr-2019 16:42:49 EDT Don Romano (alt)

   QAM is a good example of a practical application of complex numbers:

   https://en.m.wikipedia.org/wiki/Quadrature_amplitude_modulation

   Basically, if you have a carrier wave, you can encode a vector in it as A = x cos(phi) + y sin(phi). To encode data, you assign different symbols to different vectors. Since the rotation of your vector will depend on the phase angle of your carrier wave, you typically include a phase reference along with it, for example, an unmodulated carrier wave to serve as a pilot tone for phase alignment.

   1. Don Romano (alt) (thor@noagendasocial.com)'s status on Sunday, 21-Apr-2019 16:52:18 EDT Don Romano (alt)

      in reply to

      If you have a QAM demodulator, you can actually demodulate most signals. FM will look like a vector that rotates with the signal amplitude. AM will look like a vector that grows or shrinks with the signal amplitude. PSK will look similar to FM but with discrete phase steps. If you have a whole bank of QAM detectors, you can demodulate OFDM, which is basically a stack of QAM carriers spaced apart just enough to avoid crosstalk. It's used in the high-speed modes of WiFi and 4G.