# Finding Fourier series coefficient a0

## Homework Statement

We're given this 'interactive page' that gives us the values, so T=2.8066, W=0.9542 and A=8.5988 and then told to find a0, b0, a1, b1, a3, b3, Total Power and 3rd harmonic power.

## Homework Equations

Cn given above and:
a0=1/T $$\int s(t) dt$$ integrating from 0 to T.

Also, c0=a0.

## The Attempt at a Solution

I can't find a way to use the Cn forumla given, since sinc(x)=sin(PIx)/PIx, where x=nfW, and you can see why I can't use it if I want to find c0. So I go to the usual formula for a0, involving the integral, i use that and end up with: a0=8.5988 which is my amplitude and the web page where we have to input our values tells me that I'm wrong. I don't know what I'm doing wrong here?

I can find a1 and a3 easily from the Cn formula (and since Cn=An/2), all the b values=0, since it's an even signal, so I'm stuck with a0?

Also how would I go about to find the total power?

Thanks.

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Ok I figured out a0...i just forgot that a zero in the denominator means that the value goes to infinitiy, and the sin of infinity goes to 1..

That leaves the total power then?

vela
Staff Emeritus
Homework Helper
Ok I figured out a0...i just forgot that a zero in the denominator means that the value goes to infinitiy, and the sin of infinity goes to 1..
That makes no sense.
That leaves the total power then?
What formulas do you have for computing the total power of a signal?

^^You're right it doesn't make sense, and it isn't right..I thought that was the limit of sin(x) as x goes to infinity but I forgot that it's actually not defined. But taking that 'reasoning' solved my problem with finding a0.

As for the power of the signal, I figured it out (well I found the formula).

If the numerator and denominator of a fraction both tend to zero, you can use L'Hopital's rule to find the limit. This is often useful for finding the a0 coefficient in fourier series. I believe you can also use a taylor series method to find a0 also.

L'Hopitals rule is quite simple to use, so if you haven't tried it it might be worth looking it up.