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I have a truncated data set that I need to transform, for example:

 x=linspace(0,5,256);
 y=cos(pi*x).*exp(-x.^2/8);
 tr=(tanh(linspace(-20,100,numel(x)))+1)/2;
 plot(x,y.*tr)

enter image description here

N=2^9;
df=1/(N*dq/sqrt(2));         
fvec=(0:df:df*(N-1));
h=window(@hamming,numel(x))';

f=idct(y,N);
f_truncated=idct(y.*tr,N);
f_truncated_hamming=idct(y.*tr.*h,N);

plot(fvec,f,fvec,f_truncated,fvec,f_truncated_hamming);
xlim([0 10]);

enter image description here adds the expected ringing artifact. My problem is the nearest side lobes .. I tried adding a window filter such as hamming etc, but I still have this ringing artifacts. Any advice will be appreciated...

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