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jamesj posted the most wonderful lecture let me see if i can find it

well no i can't. when he is on, ask him

...He has so many answers. Wow.

lol what did you expect?
not so much math?
what is your interest in fourier tranform?

any function can be expressed as a infinite sum of waves

neat.

How does the transform decompose those waves? Perhaps this is where the math kicks in, lol...

to get an even function you need cosines,
and many functions will need both

and transforming into the imaginary domain somehow gives us magical frequency values? sweet.

the fact that it has the imaginary component just says the wave is Waving in and out of phase

I understand complex waveform but I guess I'm just not sure how the transform *decomposes* it.

well the transform equation decomposed the original function into even and odd bits

Always better to have your orthogonal base to be also orthonormal, makes things much much easier!

Wow, man. That's awesome. Exactly what I was looking for. Thank you.

No problem at all :)