Fourier Analysis Help

cunnins4

Hi lads, could someone point me in the right direction about question 3 here???

I don't want the answer, or anything similar, but if someone could explain the question to me i'd very much appreciate it. I'm struggling with Fourier's stuff at the moment and I can't make any sense of the lecturer's notes. I've read up on fourier analysis on wiki etc... and I understand the transform and its similarity to Laplace, but the co-efficients bit is way over my head.

Cheers in advance.

Stephen

EDIT: Whooops, can't edit the title now, but obviously it should be FOURIER, not FOURIE!

Michael Collins

Draw the frequency response of the system (the piecewise defined function you're given). Now figure out the fundamental frequcency (you're given the period...). Now each of the ak's is the amplitude of a harmonic, which must be an integer times the fundamental. Now you can work out which ones get through...

See how you get on with that...

apeking

Third year engineering maths in trinity??

i remember those days, and i have forgotten it all too

Sorry

cunnins4

Michael Collins wrote: »

Draw the frequency response of the system (the piecewise defined function you're given). Now figure out the fundamental frequcency (you're given the period...). Now each of the ak's is the amplitude of a harmonic, which must be an integer times the fundamental. Now you can work out which ones get through...

See how you get on with that...

I'd gotten that far with the fundamental frequency (8pi?) So since ak must equal zero (is this some sort of low pass filter?) k must be anything over 50pi so the answer is k>56pi for ak=0? is that right?

my sketch looks like this:

Michael Collins

Yep, you pretty much have it. k will actually be the harmonic number though, so what harmonic does 56pi correspond to?

Yes this is an ideal lowpass filter. It blocks everything with an angular frequency > 50pi rad/s. You're told that the input and the output are identical...so the only way that can be the case is if the input doesn't contain any harmonics greater than 50pi rad/s (otherwise they would be filtered out and the output would be different).

Does this make sense?

cunnins4

Oh, okay, so that would make it for k>= 7 as in the 7th harmonic or greater?

Michael Collins

Yes, exactly.

cunnins4

oh hoorah! Thanks for the help man, much appreciated!

Tune in next week for next week's homework, same bat time, same bat channel!:D

Fremen

Goddamn it, that's "same bat time, same bat channel".

Must you butcher the classics so?

cunnins4

Fremen wrote: »

Goddamn it, that's "same bat time, same bat channel".

Must you butcher the classics so?

Sorry, my daddy had me learning multivariate calculus when all the other kids were watching batman etc....

I edited the butchery.