There are two functions f(t) and g(t); t is the independent variable.(adsbygoogle = window.adsbygoogle || []).push({});

The distance between the two functions will be given by [1/2pi integral{f(t)-g(t)}^2 dt]^1/2 between -pi and +pi.

Apparently, this distance also is the fourier coefficient of each term in the fourier

expansion of a periodic function f(t) such that it is closest to f(t).

Why is this so ?

why is not the distance given by f(t)-g(t) simply ?

i.e 1/sqrt(2pi) integral{f(t)-g(t)}dt between -pi and +pi.

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# Distance of functions and fourier coefficients

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