如題: A periodic function f(x)=f(x+T) is approximated by the finite sum of
k
it's Fourier series f(x)=Pk(x)=Ao+Σ[Ancos(nWox)+Bnsin(nWox)]
n=1
Wo=2π/T and the total mean square error is defined as
T/2 2
Ek=1/T ∫ [f(x)-Pk(x)] dx. If the coefficients in Pk(x) are determined by the
-T/2
Euler Formulae,prove that the approximation has the "least total mean square
error"property.
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