This high-frequency component can then be filtered out, leaving the original audio frequency signal.
If m(t) is the original message, the AM signal can be shown to be Multiplying the AM signal x(t) by an oscillator at the same frequency as and in phase with the carrier yields which can be re-written as After filtering out the high-frequency component based around cos(2ωt) and the DC component C, the original message will be recovered.
There are many other kinds of product detectors as well, which are practical if one has access to digital signal processing equipment.
If m(t) is the original message, the AM signal can be shown to be Multiplying the AM signal by the new set of frequencies yields After filtering out the component based around cos(4ωt) and the DC component C, the original message will be recovered.
On the other hand, the envelope detector is a simple and relatively inexpensive circuit, and it can provide higher fidelity, since there is no possibility of mistuning the local oscillator.