Need some help generating White Noise Source

clear all
close all
clc
tic


L=10; %[m] Fiber length
PS=1;
n=1.45;
eps0=8.854e-12; % [F/m] Vacuum permittivity
mu0 = 4*pi*1e-7;%[H/m] Vacuum permeability
c=2.9979e8; % [m/sec] Speed of light
Z0=sqrt(mu0/eps0);   %[Ohm] Vacuum impedance
dt = 6e-12; dz=dt*c/n;    %Spacial and Temporal step sizes.
%dz=2.5e-4;
Fs=1/dt;


N=round(L/dz); % Fiber length discretization

T=10*2*L*n/c;   %time taken for 10 round trips
Nt=round(T/dt);
%% material characteristics

A=80e-12;   %[m^2] fiber's effective area


I1_0=PS/A; 

% figure;
FA=(-Nt/2:Nt/2-1)*Fs/Nt;

fc=3e9;
X = randn(1,Nt);  %random noise generation
Y1 = 10*lowpass(X, fc, Fs, Steepness=0.8); 

ypm1 = 1.2743e+06*exp(1i*Y1);
 figure;
 plot(FA,abs(fftshift(fft(Y1/Nt))));
 xlim([-20e9 20

e9]);

figure;
semilogy(FA,(2*n*c*eps0*A*abs(fftshift(fft(ypm1/Nt).^2))))

I am trying to generate White noise source for my phase modulation technique.

The procedure is to pass the signal through a rectangular band filter to imprint the sinc envelope onto the waveform.

Likewise I have generated random noise and passed through low pass filter of 3GHz but the fft of the product is not upto the figure.

Can anyone suggest any changes.

[Umar]

Hi @Yogesh,

Please see my response to your comments, “I am trying to generate White noise source for my phase modulation technique.The procedure is to pass the signal through a rectangular band filter to imprint the sinc envelope onto the waveform.”

L = 10; % [m] Fiber length

PS = 1;

n = 1.45;

eps0 = 8.854e-12; % [F/m] Vacuum permittivity

mu0 = 4 * pi * 1e-7; %[H/m] Vacuum permeability

c = 2.9979e8; % [m/sec] Speed of light

Z0 = sqrt(mu0 / eps0); %[Ohm] Vacuum impedance

dt = 6e-12;

dz = dt * c / n; % Spacial and Temporal step sizes

Fs = 1 / dt;

N = round(L / dz); % Fiber length discretization

T = 10 * 2 * L * n / c; % Time taken for 10 round trips

Nt = round(T / dt);

% Material characteristics

A = 80e-12; % [m^2] Fiber's effective area

I1_0 = PS / A;

% Generating White Noise

white_noise = randn(1, Nt); % Generating white noise signal

% Phase Modulation Technique

phase_modulated_signal = sin(2 * pi * white_noise); % Phase modulation

% Rectangular Band Filter to Imprint Sinc Envelope

sinc_envelope = sinc(linspace(-5, 5, Nt)); % Generating sinc envelope

filtered_signal = conv(phase_modulated_signal, sinc_envelope, 'same'); % Filtering the signal

% Plotting

figure;

subplot(3,1,1);

plot(white_noise);

title('White Noise Signal');

subplot(3,1,2);

plot(phase_modulated_signal);

title('Phase Modulated Signal');

subplot(3,1,3);

plot(filtered_signal);

title('Filtered Signal with Sinc Envelope');

So, in the provided modified code, generated white noise using randn function. Performed phase modulation on the white noise signal, created a sinc envelope using the sinc function, filtered the phase-modulated signal with the sinc envelope using convolution and finally, plot the white noise signal, phase-modulated signal, and the filtered signal with the sinc envelope. Please see attached plot.

Hope this is what you were looking for.