Editing Envelope detector (section)

== Definition of the envelope ==
[[Image:analytic.svg|thumb|300px|right|A signal in blue and the magnitude of its [[analytic signal]] in red, showing the envelope effect]]
{{Main|Envelope (waves)}}

Any [[amplitude modulation|AM]] or [[frequency modulation|FM]] signal <math>x(t)</math> can be written in the following form
: <math>x(t) = R(t) \cos ( \omega t + \varphi(t) ) \,</math>

In the case of AM, φ(''t'') (the phase component of the signal) is constant and can be ignored. In AM, the [[carrier frequency]] <math>\omega</math> is also constant. Thus, all the information in the AM signal is in ''R''(''t''). ''R''(''t'') is called the ''envelope'' of the signal. Hence an AM signal is given by the function
: <math>x(t) = (C + m(t)) \cos(\omega t) \,</math>
with ''m''(''t'') representing the original audio frequency message, ''C'' the carrier amplitude and ''R''(''t'') equal to ''C'' + ''m''(''t''). So, if the envelope of the AM signal can be extracted, the original message can be recovered.

In the case of FM, the transmitted <math>x(t)</math> has a [[constant envelope]] ''R''(''t'') = R and can be ignored. However, many FM receivers measure the envelope anyway for [[received signal strength indication]].