# What is the Frequency Spectrum of a Modulated Carrier?

*Most recent answer: 11/30/2016*

- Suresh (age 63)

Kanpur, India

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( ω_{1}t) and B = cos( ω_{2}t) where ω_{1} is the carrier frequency and ω_{2} is the signal frequency. Then the modulated signal is S = A*B*cos(ω_{1}) *cos(ω_{2}) = A*B*[cos(ω_{1}+ω_{2}) + cos(ω_{1}-ω_{2}) ]/2. So there are two frequencies in the result: Ω_{1} = ω_{1}+ω_{2}_{ } and Ω_{2} = ω_{1}-ω_{2} .

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)*