Thread: fourier transforms

just wondering if some1 can help me, ive almost understood but just need to finish things off.

thanx
Edgar

1)I dont fully understand what the curly F is doing in the fourier transforms. Is it simply that
curly F of f(x) means f hat (x)? could some1 please shed some light on the function of the curly f.

2) why is it true that f(x) all hatted = f hat (k)?

3) i dont fully understand the sine and cosine transforms can someone please explain them to me.

Thanx

What are you talking about?

What hats?

You need to post your definition of Fourier Transform.

Originally Posted by edgar davids

just wondering if some1 can help me, ive almost understood but just need to finish things off.

thanx
Edgar

1)I dont fully understand what the curly F is doing in the fourier transforms. Is it simply that
curly F of f(x) means f hat (x)? could some1 please shed some light on the function of the curly f.

2) why is it true that f(x) all hatted = f hat (k)?

3) i dont fully understand the sine and cosine transforms can someone please explain them to me.

Thanx

I think I get your question now.

"Curly F" is that the same one that appears in my image upload?

I am sure you know what a Laplace transform is, right?

It is the same thing.

When you are asked to find Laplace transorm of sin(x) you sometimes write it as,
Curly L(sin(x)).

Same thing here, it just represents an operation on a function.

A Fourier transform (by analogy a Laplace Transform) is a function which maps functions that maps real numbers (or complex) into real numbers into other functions which map real numbers into real numbers.