# Homework Help: Question on finding the Fundamental Period of a periodic FM signal

1. Sep 19, 2009

### guitarguy1

1. The problem statement, all variables and given/known data

s(t)=13*cos(2000*pi*t + 100*sin(8*pi*t))

Determine the fundamental period of this signal, i.e., the shortest period.

2. Relevant equations

x(t)=A*cos(2*pi*f(c)*t + a*sin(2*pi*f(m) + phi))

A=13; f(c)=1000; a=100; f(m)=4; phi=0

Inverse Euler's - A*cos(omega*t + phi) = A/2*exp(j*omega*t)exp(j*phi)+A/2*exp(-j*omega*t)*exp(-j*phi)

3. The attempt at a solution

My normal approach to summed sinusoidal signals doesn't seem applicable here. Determining the fundamental period by looking at the two frequencies wouldn't help as the sin is incorporated into the cosine function rather than added or multiplied like is more commonly seen. I'm not sure if I should use Inverse Euler's to get s(t) into a form where I can plot the spectrum to find the frequency. This seems like it would be very difficult and might not even work. I was wondering if there is any simpler formula or rule that can help me find the fundamental period of a sum of sinusoids taking this form. Or could I still simply find the GCD of f(c) and f(m) and use that fundamental frequency to find the fundamental period? Thanks.

edit: If it's any help I've determined the fundamental frequency to be 1400 hz and thus the fundamental period to be .000714 s by running it through matlab. I'm just not sure how to show that mathematically.

Last edited: Sep 19, 2009