How to create a random input with Butterworth band filter and specific PSD

Hello,

I am currently attempting to create a random time input for vibration that is in accordance with a given PSD chart. I am attempting to limit this chart based on a given high-pass and low-pass frequency using a Butterworth band pass filter. I have quite a few problems, but my biggest issue is that, after I've created by Butterworth filter, I don't know how to create my random time input and then take a reliable PSD of it. Here is what I have so far:

if true
t=180;          %Experiment time
Fs=200;         %Sample frequency
N=t*Fs;         %Total number of points to be generated
GPmax = 5.18;   %max PSD
f1=0.89;
f2=11.22;
f3=2.0;
f4=2.7;
H=fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2',f1,f3,f4,f2,50,0.5,50,Fs);
D = design(H,'butter');        
y=filter(D,GPmax*wgn(N,1,GPmax));
h = spectrum.welch;
Hpsd = psd(h,y,'Fs',Fs);
plot(Hpsd);
end

How can I use this Butterworth to create my random time input? I feel like wgn may not be getting the job done, else my welch PSD isn't an accurate representation of my PSD.

Thanks in advance for any help!