# Fourier series - addition of cosine and sine of different frequencies

• October 28th 2010, 04:55 PM
afried01
Fourier series - addition of cosine and sine of different frequencies
I need to find the Fouier series of the following:

f(t) = cos(4t) + sin(6t)

I know what they are individually, but for both of them added together I get a period of (pi / 2) / (pi / 3) = 3 / 2 so the period is 6,,, correct? The fourier series by themselves are just cos(4t) and sin(6t) repectively. Do you just place this expression in the formulae with T = 6? That's a lot of messy math. Any help on how to do this would be very much appreciated.

In addition, when I graph this on Matlab the period is smaller than 6. It looks a little bigger then 3. Any hints on what's going on?

Thanks
• October 28th 2010, 10:23 PM
afried01
OK,, I've been taught, maybe the wrong way, that in order to find a common period of two sums such as cos(4t) + sin(6t) you do the following:

Find periods: 2pi / 4 = pi / 2 -- This is first period T1

Next,, 2pi / 6 = pi / 3 -- This is second period T2

Now T1 / T2 must be rational so (pi / 2) * (3 / pi) = 3 / 2 which is rational. Now find LCM(3, 2) which is 6.

What is wrong with this? Why would a graph show it is pi which is an irrational number?(Headbang)
• October 29th 2010, 12:05 AM
CaptainBlack
Quote:

Originally Posted by afried01
OK,, I've been taught, maybe the wrong way, that in order to find a common period of two sums such as cos(4t) + sin(6t) you do the following:

Find periods: 2pi / 4 = pi / 2 -- This is first period T1

Next,, 2pi / 6 = pi / 3 -- This is second period T2

Now T1 / T2 must be rational so (pi / 2) * (3 / pi) = 3 / 2 which is rational. Now find LCM(3, 2) which is 6.

What is wrong with this? Why would a graph show it is pi which is an irrational number?(Headbang)

Except the period has to be an integer multiple of $\pi$ (and that integer is the $\gcd(2,3)=1$)

CB