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basic question on AM modulation

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elecfan

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can we consider AM modulation as multiplication of two signals?
 

can we consider AM modulation as multiplication of two signals?
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Clearly yes, see this explanation https://en.wikipedia.org/wiki/Amplitude_modulation

Two simple multiplication cases can be distinguished

y(t) = [1 + m(t)]*c(t) (regular AM with carrier, as used in broadcast)
y(t) = m(t)*c(t) (double-sideband modulation with suppressed carrier)
 

in the first case we will have:
y(t) = c(t) + c(t).m(t) (multiplication of the two or convolution?)
and also in the second case.

in the first case we will have wc, (wc+wm) and (wc-wm) in frequency band
and in the second case just wc+wm and wc-wm.

is this right?
 

It is multiplication.

y(t)=[ 1 + m(t)].c(t)

m(t)= cos(2*pi*fm*t)
c(t)= cos(2*pi*fc*t)

Substituting the above in y(t), and applying a trigonometric identity, you can find terms that contain fc+fm and fc-fm.
The purpose of this is to frequency translate the message signal. The way to do it is multiplication.
 

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