I recently came to the conclusion that I should learn something more about signal processing and started reading the first pages of both Andy Farnell tutorials and Synth Secrets by Gordon Reid.

The basics of Amplitude Modulation seem clear to me. When multipling an oscillator signal (the carrier) for another one (the modulator), I get a new waveform which includes three frequencies: the carrier, the sum (carrier + modulator) and the difference (carrier - modulator).

It works fine, but something goes wrong when trying to make a reverse test. I am expecting that if I sum up three oscillators (carrier frequency, sum frequency, difference frequency) the resulting wave should sound like the one I get from the amplitude modulation, but it doesn't. It is the same (and the waveform correspond as well) only if I mute the carrier frequency. Why is this happening?

As a total beginner I'm pretty sure I'm missing some simple logic here. Attached is a test patch.

Thanks in advance for your patience.

http://www.pdpatchrepo.info/hurleur/am.pd

the frequencies are the same, but the phase is changed.

i just did trial an error, trying to get the correct phase, but no luck. however, if you send floats into the right inlets your [osc~] objects, you will be able to see how the phase affects the sound.

What you're doing is actually ring modulation. When the modulator is bipolar, then it is considered ring mod, and you end up with only sidebands; the carrier frequency disappears. To make it AM, you should make the modulator unipolar positive (i.e., in the range of [0, 1]). Then you'll keep the carrier plus the sidebands. And the sidebands will have half the amplitude of the carrier.

I didn't know about the unipolar thing. I changed the modulator [osc~] output into a range of [0, 1] and then adjusted the amplitude of the sidebands. It works perfectly and keeps both the sidebands and the carrier.

Thank you!