Filtering white noise with first and second order filter

Hi everyone

I have a question about filtering white noise with a discrete tf like below :

but i dont know use data or frequency for axis x ?

I use data and I have something like this

my x axis is data and my y axis is amplitude

do you think is it correct or i should do it with frequency?

if i am wrong what should i do ?

Thanks

my code is

clc 
clear all 
close all 

dt = 0 ;
T = 100;
ts = 0.1;
t = dt:ts:T-ts;
N = numel(t) ;  %number of data


u = randn(N,1);
H1 = tf((sqrt(3)/2),[1 0.8],ts)  %first order filter 

y= zeros(N,1);

a = 0.8;
b = sqrt((3)/2);
for i =2:T-ts
    
    y(i) = a*y(i-1) + b*u(i-1);
    
end
plot(u)
hold on 
plot(y)
title('Filtering White Noise')
ylabel("Amplitude")
xlabel("Data")
legend("white noise","filtered white noise")

[Mathieu NOE]

hi

look at filter and filtfilt functions

I prefered to do the demo on a unity gain (dc gain = 1) filter so it appears evident that the filtered signal is lower in amplitude

clc 
clear all 
close all 
dt = 0 ;
T = 100;
ts = 0.1;
t = dt:ts:T-ts;
N = numel(t) ;  %number of data
u = randn(N,1);

% discrete filter num and denominator
% num = [sqrt(3)/2 0];
a = 0.8;
num = [1-a 0]; % unity gain LP filter
den = [1 -a];

y = filter(num,den,u);

plot(t,u,'b',t,y,'r')
title('Filtering White Noise')
ylabel("Amplitude")
xlabel("Data")
legend("white noise","filtered white noise")