Please help.... Fourier analysis

jtiernan

I know it is to do with the formula



But dont know how to do it..

Any advise?

tdow

ok i might be wrong here but it looks like you're leaving out part of the question. it looks like you should be told what f1(t), f2(t), f3(t) ... are , and there will be some relationship between them e.g. f2(t) = 2f1(t), so in this case, all you'd have to do is multiply the fourier series for f1(t) by 2 to find the fourier series for f2(t)

Michael Collins

Yep you need to know what the other functions are! My guess is that the other functions are probably related to the given one as tdow said, either by a scaler multiple or change of DC component or change of period or something - so you probably won't have to actually compute a Fourier series at all, just apply a few simple relationships.

If you want us to help you further you'll have to post up the full question!

jtiernan

I'm sorry I did not post the first part of the question. I pasted it wrong.




I thought I could just solve f2, f3 etc. individually and wondered why he solved and referenced f1?

Michael Collins

jtiernan wrote: »

I thought I could just solve f2, f3 etc. individually and wondered why he solved and referenced f1?

You could do that but that would be a lot of effort, when in fact you don't have to. Take a look at the f2(t) for example, here the period is the same as f1(t), all that is different is f1(t) has been doubled (so you multiply it by 2) and a DC offset has been added (so you add that on too).

So the relationship is: f2(t)=2f1(t) + pi

So just apply this to the Fourier series that you're given. Again it's a similar process for the other series', just remember that the period of the other ones isn't the same as f1(t)...so you'll have to accomodate that - i'll let you think about this part yourself! (Hint: try a change of variables t=u*v, where you pick u as appropriate).

This is how Fourier Series are usually done in practise, from a table or book of basic ones you can apply a few simple changes like this to get quite a large superset.

Hope this helps anyway.

jtiernan

Thanks a million tdow and michael collins. That has been excellent assistance. I am not sure how to physically multipy and add pie to the series but I will have a go at it and am surely a lot better off than I was.