On 26 Feb, 20:54, "tkremund98" <tkremun...@hotmail.com> wrote:
> This is just a question about Gibb's effect. Is Gibb's Effect is present in
> stationary data?

Gibbs' effect has nothing to do with whether data are
stationary, but with properties of the Fourier transform
around discontinuities.

The problem is that the Fourier transform converges
in the mean square sense, i.e. that the L2 reconstruction
error (view with fixed-width font)

n-1
e_n^2 = integral |f(t) - sum A_n exp(j w_n t)|^2 dt
k=0

vanishes as n -> infinity. However, this convergence
in the mean does not ensure *pointwise* convergence,
since pointwise convergence is expressed in terms of
the L1 norm:

n-1
E_n = |f(t) - sum A_n exp(j w_n t)|
k=0

This discrepancy between pointwise and mean convergence
becomes particularly important at dicontinuities in f(t),
which is what causes Gibbs' phenomenon.

Rune