low pass filter coding that received white noise as a input

I want to create a low pass filter exactly

w0/ (s+ w0)

This filter received white noise of spectural density as i/p and give an output.

Note: w0 is the natural frequency of the system.

Answer 1

[William Rose]

@Muhammad Asad,

You have specified a low pass filter with a cutoff frequency of radians per unit time. Since you did not specify a filter order, or other filter requirements, we will use the simplest low pass filter:

where , where is the sampling rate, in samples per unit time.

Example: Sampling rate = . Desired lowpass filter cutoff frequency = radians/s.

%% Define constants
fs=100;             %sampling rate (Hz)
w0=10*2*pi;         %cutoff frequency (radians/s)
N=100;              %number of points in signal
%% Define input signal and time vector
t=(1:N)/fs;         %time vector
x=randn(1,N);       %input signal=Gaussian white noise
%% Filter the input signal
alpha=w0/(w0+fs);
y=zeros(1,N);       %allocate array for y
y(1)=0;             %initial value for y
y(2:N)=alpha*x(2:N)+(1-alpha)*y(1:N-1);  %filter the signal
%% Plot results
plot(t,x,'-r',t,y,'-b'); 
xlabel ('Time (s)'); legend('Input','Output'); title('Lowass filter')

Good luck.