History of Amplitude modulation

	Revision 24 . . December 7, 2001 7:07 pm by Zundark [don't put *all* the maths in italics, just the variables]
	Revision 23 . . (edit) December 7, 2001 7:03 pm by The Anome [fixed mistake in formatting]
	Revision 22 . . December 7, 2001 7:01 pm by The Anome [copyedit: put math in italics, as per other aticles]
	Revision 21 . . December 6, 2001 12:35 am by The Anome [the 'wrong' sideband is often only partially filtered out - adjusted sentence. s/side bands/sidebands/]
	Revision 20 . . December 5, 2001 4:17 am by Gareth Owen [direct link to [[SSB]]]
	Revision 19 . . (edit) December 4, 2001 7:20 am by The Anome [used colon indent to get rid of monospacing]
	Revision 18 . . December 4, 2001 6:39 am by The Anome [rejigged maths example typography, hopefully without breaking it]
	Revision 17 . . December 4, 2001 6:32 am by The Anome [greek omega; 'often' not always filtered out]
	Revision 16 . . December 4, 2001 4:12 am by Ap [Incorporated discussion into main article]
	Revision 15 . . (edit) December 3, 2001 1:58 am by The Anome
	Revision 14 . . December 3, 2001 1:58 am by The Anome [mentioned bandwidth expansion, -> SSB]
	Revision 13 . . December 3, 2001 1:53 am by The Anome [-> modulation]
	Revision 12 . . (edit) December 3, 2001 12:42 am by The Anome [term in bold]
	Revision 11 . . (edit) October 22, 2001 6:18 pm by (logged).37.81.xxx [link fix]

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Difference (from prior major revision) (no other diffs)

Changed: 15c15

Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency Ω is

Suppose we wish to modulate a simple sine wave on a carrier wave. The equation for the carrier wave of frequency Ω is

Changed: 17c17

:c(t) = C sin(Ωt)

:c(t) = C sin(Ωt)

Changed: 21c21

:m(t) = M sin(ωt + P)

:m(t) = M sin(ωt + P)

Changed: 23c23

Amplitude modulation is simply adding m(t) to C, the amplitude modulated signal is than

Amplitude modulation is simply adding m(t) to C, the amplitude modulated signal is than

Changed: 25c25

:y(t) = (C + M sin(ωt + P)) sin(Ωt)

:y(t) = (C + M sin(ωt + P)) sin(Ωt)

Changed: 27c27

The formula for y(t) above may be written

The formula for y(t) above may be written

Changed: 29c29

:y(t) = C sin(Ωt) + M cos(P - (ω-Ω)t)/2 - M cos(P + (ω+Ω)t)/2

:y(t) = C sin(Ωt) + M cos(P - (ω-Ω)t)/2 - M cos(P + (ω+Ω)t)/2

Changed: 31c31,33

So the broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from Ω. These are known as sidebands. In general a signal of frequency ω broadcast with a carrier wave frequency Ω will produce waves of frequency Ω +/- ω and, as long as the broadcast (i.e. the carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap stations will not interfere with one another. In practice one of the sidebands is superfluous and is often wholly or partially filtered out before broadcast in order to reduce congestion of the airwaves (see single sideband modulation).

So the broadcast signal consists of the carrier wave plus two sinusoidal waves each with a frequency slightly different from Ω. These are known as sidebands. In general a signal of frequency ω broadcast with a carrier wave frequency Ω will produce waves of frequency Ω +/- ω and, as long as the broadcast (i.e. the carrier wave) frequencies are sufficiently spaced out so that these side bands do not overlap stations will not interfere with one another. In practice one of the sidebands is superfluous and is often wholly or partially filtered out before broadcast in order to reduce congestion of the airwaves (see single sideband modulation).