Carrier and Sidebands
Why does amplitude modulation of a carrier signal produce
both an upper and a lower sideband?
When you amplitude modulate a carrier, you are mixing a
radio-frequency wave with an audio-frequency wave (the audio signal).
The mixing of two frequencies produces both the sum and difference of
the frequencies, for the simple reason that:
cos(w1 t) cos(w2 t) = 0.5 ( cos[(w1+w2)t] + cos[(w1-w2)t] )
w1 is the carrier frequency, w2 is the audio frequency. You see
the two sidebands (w1+w2 and w1-w2) right there. Typically most of
the power goes into the original carrier (w1) because the mixing isn't
very efficient. So you get three signals.
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Update: June 2012