How to add Noise, with Zero mean, to Transfer Function or to Input signal ?

I have worked with rand function to introdue noise and thats perfectly fine. But my question is different and I will like if someone can comment it on.

I have a transfer function and input signal. And from this I calculate my output signal and then convert it to time domain.

NOTE: The correct code is given in attached file and latex line, incase below copied reverts few lines.(weird problem happens when i save my post, it reverse few lines)

How can I add a noise to input signal or transfer function, rather then output signal, which is in S domain?

Q=5e-15;  
QTIME=4e-9; % Max 11ns
I=Q/QTIME;

to1=1e-9;
to2=to1+QTIME;

%%% Input Signal Laplace Transform
syms s;
x1s=(exp(-s*to1))*1/s-(exp(-s*to2))*(1/s);
I=Q/QTIME; 
x1s=I*x1s;
x1t=ilaplace(x1s);

%%%%% DA3 Transfer Function %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
R1da3=2.45e3/2;
R2da3=9.77e3/2;
C1da3=92e-12;
syms r1da3 r2da3 c1da3;
tf_da3=s*c1da3*r2da3/(1+s*c1da3*r1da3);
tf_da3=0.1+tf_da3./(1+s/(2*pi*150e6));
tfda3=subs(tf_da3,{r1da3,r2da3,c1da3},{R1da3,R2da3,C1da3});
pretty(tfda3);

wu=1.2868e+08;
syms t;
T=50/wu;
N=100;
time=1:1:N;

time=T*time/N; %time=T*(time/N);
da3=x1s*tfda3;
da3s = ilaplace (da3);
da3t = subs (da3s, {t}, {time});

plot (time * 1e9, da3t, '-k' , 'LineWidth' , 2);
hold on

[darova]

• NOTE: The correct code is given in attached file and latex line, incase below copied reverts few lines.(weird problem happens when i save my post, it reverse few lines)

There is no need of LaTeX "code". Only LaTeX formulas or equations