Add impulsive noise generated by ε mixture of Gaussian noise

I have to add noise to a signal following a function on a scientific paper. The noise, like specified in the title, is generated by ε mixture of Gaussian noise that has a porbability density function of:

I have try to translate this function into a code, and I think that is right, but I am very insecure about this kind of things and I want to be 100% sure that what I have done is correct.

Explanation of the function: ϕ(y) is the probability density function of a Gaussian random variable with zero mean and unit variance. σ2 is tipically much larger than σ1. ε is a weight, wich controls the distribution of the two ϕ, the background noise and the impulse noise, respectively.

My Attempt:

clc;
close all;
clear;
load("100m.mat"); % load signal
y = val; % MY Signal
L = length(y); % length of the signal
E = 0.1 + (0.5).*rand(1); % epsilon (range 0.1-0.5)
s_1 = 10; % sigma1 (σ1) 
s_2 = 100; % sigma2 (σ2)
noise = (1-E)*s_1.*randn(L) + E*s_2.*randn(L); % generated noise
yn = y + noise; % noisy signal 

[Sabaudian]

I'm just asking for a check. I just need to know if what I wrote is right or wrong. thank you

Answer 1

[Abhimenyu]

Hi Sabaudian,

I understand that you want to add noise to your signal according to the given equation. The provided code does not implement the gaussian random vector correctly. Please refer to the code below for better understanding:

clc; 
clearvars; 

load("100m.mat"); % load signal 
y = val; % MY Signal 
L = length(y); % length of the signal 

E = 0.1 + (0.5 - 0.1) * rand % Random value of k between 0.1 and 0.5 
s1 = 10; % Value of s1 
s2 = 100; % Value of s2 

% Generate noise based on the probability density function 
f = @(y, s) exp(-(y.^2) ./ (2 * s)) ./ (sqrt(2 * pi*s));  

% Gaussian probability density function 
noise = (1 - E) * f(y / s1, 1/(s1^2)) + E * f(y / s2, (1/s2^2)); 
% Calculate the noise based on the given PDF, phi(y) has 0 mean and unit var, so phi(y/s) will have 0 mean and 1/s^2 var 

% Add noise to the signal 
yn = y + noise; % noisy signal 

I hope this helps!

Thank you,

Abhimenyu.