I was reading the better explained article introduction to Fourier Transforms - sounds pretty interesting stuff, I was wondering if would be possible to explain this idea mathematically to 17-18 year old maths students - I've not seen anything sufficiently at that level, so I'm wondering if it is possible. I'm not quite sure on it all myself yet, hence this thread ;)
There's some discussion on fourier transform here: http://ift.tt/1pzVPpn
About halfway down there is an example of a function:
f(t)=sin(t)+0.13sin(3t)
Now, with a fourier transform his is converted from a time vs f(t) graph to a graph of the frequency of the function - but what is this new graph plotted against? Time? f(t)? f hat (t) ?
What does frequency of a f(t) time function actually show you? I understand frequency in terms of affecting the repeating period of a periodic function - but how does this relate to the f(t) graph above?
Which version of the fourier transform is then best to use for the example above? The wiki version is:
\hat{f}(\xi) = \int_{-\infty}^\infty f(x)\ e^{- 2\pi i x \xi}\,dx, for any real number ξ
So, I could convert f(t) into the exponential form and simplify, integrate and evaluate the improper integrals - but how do I arrive at my number ξ to plug in? Isn't this just any real number? Will the new transform have the same period as the original function or not?
Reading this back, that's quite a lot of questions, guess I don't understand this too well!
Thanks :)
There's some discussion on fourier transform here: http://ift.tt/1pzVPpn
About halfway down there is an example of a function:
f(t)=sin(t)+0.13sin(3t)
Now, with a fourier transform his is converted from a time vs f(t) graph to a graph of the frequency of the function - but what is this new graph plotted against? Time? f(t)? f hat (t) ?
What does frequency of a f(t) time function actually show you? I understand frequency in terms of affecting the repeating period of a periodic function - but how does this relate to the f(t) graph above?
Which version of the fourier transform is then best to use for the example above? The wiki version is:
\hat{f}(\xi) = \int_{-\infty}^\infty f(x)\ e^{- 2\pi i x \xi}\,dx, for any real number ξ
So, I could convert f(t) into the exponential form and simplify, integrate and evaluate the improper integrals - but how do I arrive at my number ξ to plug in? Isn't this just any real number? Will the new transform have the same period as the original function or not?
Reading this back, that's quite a lot of questions, guess I don't understand this too well!
Thanks :)
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