Hello!

I've recently learned about the Fourier Series from the point of view of projection onto the Space spanned by the orthogonal functions 1,cos(x),sin(x),cos(2x),...

And so when I think about the Coefficients of the Fourier series, I think about how "much" of the function exists in that particular frequency. How "much" the cos(kx) or sin(kx) frequency constitutes the original function.

So now Im trying to learn about the Transform. The technique itself is of less importance, I'd like to gain an intuitive understanding about what it means... And so far all I could find is more about the technique.

Could you try to connect the dots for me, and tell me what resemblence does the transform have with the series? If you could paint in the same colors Ive mentioned about my current understanding of the Fourier Series that would be fantastic...

Thank you!