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i am trying to understand how amplitude modulation works; i have already understood that it is given by the following:

$$AM (f(t)) = cos2πτt * f(t),$$

where τ is the frequency of the sinusoid.

So for example, if i were given a function like:

$$f(t) = 100sin(100t) + 350sin(350t)$$

modulated in amplitude by the following:

$$cos200πt$$

What would the result be? I can't seem to be able to put all the pieces together.

What i've tried to do is to calculate the frequency for the cos function and put it inside the formula, however i don't know if it's the proper thing to do, and if it is, i don't know how to continue!

Does anyone know what's the right way to do it?

Thanks!

zorro
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  • do you know the correspondance of multiplication in the time domain, at the frequency domain? – Seyhmus Güngören Feb 25 '18 at 22:00
  • @SeyhmusGüngören do you mean the fourier trasform of a convolution? – zorro Feb 25 '18 at 22:06
  • yes. convolution at the Fourier domain. so what is the Fourier of a sine or cosine function? – Seyhmus Güngören Feb 25 '18 at 22:07
  • @SeyhmusGüngören sin would be 1/2i[δ(f-A) -δ(f+A)]. Cos would be similar but without the i at the denom and with a + insead of - between the deltas. Is what i’ve stated correct? – zorro Feb 25 '18 at 22:15
  • Be careful that one of the frequencies are negative and in reality cannot be realized. Whatever, yes, at the frequency domain we get a dirac delta function. now consider convolving ANY function with a dirac delta. what happens? – Seyhmus Güngören Feb 25 '18 at 22:25
  • @SeyhmusGüngören i’m not entirely sure about this, so i could definitely be wrong, but would we get a sifted signal? – zorro Feb 25 '18 at 22:40
  • yes exactly. have a look at this for mathematics: https://math.stackexchange.com/questions/1015498/convolution-with-delta-function just the answer with 3 upvotes and put $a=0$. – Seyhmus Güngören Feb 25 '18 at 22:42
  • look at here. you will see what I am talking about: https://en.wikipedia.org/wiki/Amplitude_modulation – Seyhmus Güngören Feb 25 '18 at 22:59
  • @SeyhmusGüngören thank you, this clarified a lot! – zorro Feb 25 '18 at 23:04

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