/diy/ - Do It Yourself

>>1468919
A mixer as shown in >>1468940 multiplies two signals together, and when one has a frequency much larger than the other you get that signal oscillating underneath the envelope of the lower frequency signal. But there's a mathematical simplification we can do to:
>cos(f*t) * cos(F*t)
where f and F are the two frequencies. It is equal to:
>0.5*cos((f - F)*x) + 0.5*cos((f + F)*x)
I.e. two cosines added to one another, one with a frequency slightly below the carrier and one slightly above. And the difference between the carrier and each of these frequencies is the audio frequency itself. In the frequency domain this will be visible as two bumps to either side of the carrier frequency, but the carrier frequency will also be there due to the DC component added to the initial audio wave in order to avoid zero-crossing, as illustrated in pic related. Since all audio signals you'll encounter are a superposition of sine waves, this reasoning can be extended to a case of a complicated waveform.