# Q & A: What is the frequency spectrum of a modulated carrier?

Q:
Can you please explain to me why the frequency spectrum of a carrier wave modulated in amplitude by a signal of one frequency has two additional frequencies ?Thank you so much.
- Suresh (age 63)
Kanpur, India
A:

In amplitude modulation a carrier wave is multiplied by a signal wave.   The simplest example is a sine or cosine carrier multiplied by another sine or cosine.  Let  A = cos( ω1t)  and  B = cos( ω2t) where ω1 is the carrier frequency and ω2 is the signal frequency.   Then the modulated signal is S = A*B*cos(ω1) *cos(ω2)  = A*B*[cos(ω12)  + cos(ω12) ]/2.  So there are two frequencies in the result:   Ω1 =  ω12   and  Ω2 = ω12 .

The spectrum of a frequency modulated signal is much more complicated with many more frequencies, all multiples of the modulation frequency.

For more information I recommend that you take a look at the Wikipedia article on modulation:

https://en.wikipedia.org/wiki/Modulation

LeeH

(published on 11/30/2016)