I am trying to grasp Fourier transform, I read few websites about it, and I think I don't understand it very good. I know how I can transform simple functions but there is few things that are puzzling to me.
Fourier transform takes a function from time domain to a frequency domain, so now I have $\widehat{f(\nu)}$, this is complex-valued function, so as I understand for every frequency I get an imaginary number.
-
What does this number represent, what is an interpretation of real and imaginary part of $\widehat{f(\nu)}$?
-
How can I graph $\widehat{f(\nu)}$? As I understand if function is not odd-function, $\widehat{f(\nu)}$ will have complex values and imaginary part will be different then 0. Do I need to plot it in 3d or do I just plot $|\widehat{f(\nu)}|$?. I am asking about plotting, because for example on wikipedia there is a plot of sinc function, which is fourier transform for square function. It is nice, because it is an odd-function in their case. And I am wondering about other functions.
I would be also very grateful for any useful links that can shed some light on the idea of fourier transform and some light theory behind it, preferably done step-by step.
Best Answer
The values of a frequency domain function represent how much of that frequency is "in" the function. For example, if you would take the fourier transform of a sine wave, you would get a delta function in the frequency domain: there's a lot of some specific frequency in that function.
Now, this is quite a simple way of saying it; we can deduct quite a bit more from the value, such as the "phase" of that frequency component. But it's also a bit more difficult, since for many signals the fourier transform is not composed of delta functions but a continuous function.
Don't worry too much about it, it takes a while getting used to the idea of fourier transforms. It's only now in my third year in Electrical Engineering that they really feel natural, I must say.