# Amplitude Modulation Index

Tags:
1. Jan 5, 2016

1. The problem statement, all variables and given/known data
Let's say we have a carrier signal xc(t) = AcCos(ωct)
And there is a modulating signal or we can call it the information signal xm(t) = Am Cos(ωmt) and the modulation index is given as 0.8

How to write the modulated signal? It's really confusing as many people give different definitions and can't figure out which is correct. At least this one might make me understand the basic principle as it contains an amplitude not equal to 1 in the modulating signal.

2. Relevant equations
x(t) = Ac[1 + μx(t)]cos(ωct)

3. The attempt at a solution
x(t) = Ac[1 + (μ×Am/Ac)cos(ωmt)]cos(ωct)

2. Jan 5, 2016

3. Jan 6, 2016

### Staff: Mentor

μ is defined as $\frac{A_m}{A_c}$ so you won't use both together in your expression