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are the low-pass filter and the sharp cut-off filter the same thing??

Here there is the definition of sharp cut-off filter https://en.wikipedia.org/wiki/Filter_(large_eddy_simulation) .

I tried to obtain with matlab the Fourier transform of the low-pass filter, but I noticed that I don't reach the low pass filter. What am I doing wrong?

x=-100:0.1:100
delta=5
G=sin(pi*(x+eps)/delta)./(pi*(x+eps))
H= abs(fft(G))
Tinc=0.01
Fs=1/Tinc;

freq =transpose( -Fs/2:Fs/length(G):Fs/2-(Fs/length(G)));
figure()
plot(x,G)
figure()
plot(freq,H)
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    $\begingroup$ From your link "The LES filter operation is low-pass, meaning it filters out the scales associated with high frequencies". BTW, the sharp cut-off filter is not in the link but a sharp spectral filter is which is a type of LES filter and therefore a LPF. $\endgroup$ – havakok Jul 15 '19 at 9:24
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    $\begingroup$ So is the sharp cut-off filter a type of low-pass filter? is the box filter an other kind of box filter? $\endgroup$ – Arkadiusz duka Jul 15 '19 at 9:34
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    $\begingroup$ I am not sure what you mean by a sharp cut-off filter. A google search did not yield any results on the matter, Can you support the definition of such a name with either a book or a paper? Do you mean something else maybe? $\endgroup$ – havakok Jul 15 '19 at 9:41
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    $\begingroup$ the two terms mean different specifications of a filter. "low-pass" is a type of filter as are "band-pass" and band-reject (sometimes called "notch" filters) and "high-pass". the "sharpness" of the cutoff is a quantitative specification of the degree of discrimination the filter performs between frequencies that are passed and frequencies that are rejected. $\endgroup$ – robert bristow-johnson Jul 15 '19 at 10:42
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    $\begingroup$ @robertbristow-johnson so is the Sharp spectral filter a kind of LPF? $\endgroup$ – Arkadiusz duka Jul 15 '19 at 11:30

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