# Fourier Series of cos4t + sin8t

1. May 16, 2012

### helderdias

Hi everyone,

So I was trying to calcule the Fourier Series of x(t) = cos4t + sin8t, but I'm a little bit confused. What would be ω0 in this case since I have a combination of two functions with different frequencies?

2. May 16, 2012

### HallsofIvy

I don't know what you mean by $\omega_0$ here. A Fourier series is a sum
$$\sum_{n=0}^\infty A_n sin(nt)+ B_n cos(nt)$$
Here, obviously $A_8= 1$, $B_4= 1$ and all other coefficients are 0.

3. May 16, 2012

### helderdias

I thought the series was the sum of An*cos(nw0t) + Bn*sen(nw0t)

4. May 16, 2012

### theorem4.5.9

Typically fourier series are presented as HallsofIvy posted. However, there's no reason not to include a frequency term $\omega_0$. This can simplify some expressions, and you are free to choose any $\omega_0$ you like. It's important to remember that any choice of $\omega_0$ changes the periodicity to $\frac{2\pi}{\omega_0}$.

For your example, it's clearly best to choose $\omega_0=1$