Filter out the white noise by Low pass FIR filter via window based method??

I have generated Gaussian random number sequence which is basically a white noise through the input sigma (standard deviation) and I want to filter it by using low pass FIR filter via window based (Hamming) method and I want the Gaussian shape overlap hamming window function in such a way that their spectral width (sigma) should be same or approximately same. How can I do that or check?? Also, is there any way to generate window function via input spectral width (sigma) value?? Here is the code: load oct2_fast % that only include x as time axis of length 35041 sigma=0.0237; mu=0; n2 = normrnd(mu,sigma,[length(x) 1]); fs=length(n2); Ts=1/fs; t=(0:Ts:1-Ts)'; N=50; % order of the filter wvtool(hamming(N)) cuttoff=1/2*pi*sigma;% wikipedia gaussian filter figure plot(t,n2,'c') hold on b=fir1(N,cuttoff,'low',hamming(N+1,'symmetric')); a=1; y1=filter(b,a,n2); hold on plot(t,y1,'r') legend('gaussian','filtered') grid