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A comment on Fourier transform – A math tool used in optics, MP3s, JPEGs and more (2013). Parent comment

Re:Fourier transform – A math tool used in optics, MP3s, JPE... by mturmon on Tuesday April 11, 2017 @02:28PM (#14090972)
About "why sine waves," the mantra I learned is:

"Complex exponentials are the eigenfunctions of linear systems."

This means that, if you put a complex exponential in, you get the same complex exponential out, scaled by some constant, whose magnitude we call the "frequency response". No other functional form has this property.

They are eigenfunctions, so they are orthogonal. We can represent any function in L2 using a weighted sum of them.

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Re:Fourier transform – A math tool used in optics, MP3s, JPE... by blt on Tuesday April 11, 2017 @02:33PM (#14091025)
By L2 you mean the set of square-integrable functions, right?
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Re:Fourier transform – A math tool used in optics, MP3s, JPE... by michalskop on Tuesday April 11, 2017 @05:31PM (#14092654)
Should be, see https://en.wikipedia.org/wiki/Lp_space
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Re:Fourier transform – A math tool used in optics, MP3s, JPE... by mturmon on Wednesday April 12, 2017 @01:08AM (#14094921)
Yes, and by "represent", I mean represent with respect to the L2 norm.
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