Adding and generation of shot noise to a gaussian chirp signal.

Question

majid 2021-5-15

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/831013-adding-and-generation-of-shot-noise-to-a-gaussian-chirp-signal

评论： majid 2021-5-16

Hi,

How can i adding shot noise to the gaussian chirp signal?

signal codes :

clc; clear; close all;

%--------------------------------------------------------------

fs = 1e3; dt = 1/fs; t = 0:dt:22.5e-3; % signal evaluation time

f1 = 29.25e6; f2 = 30.75e6;

c = (f2-f1)/(t(end)-t(1));

n = (-511:512)'; % Timeline

sigmas = exp(log(2):.3:log(200)); % Scales

w = exp(-.5*(n.^2)*sigmas.^(-2)); % Window Function

% Gaussian Chirp

chirps = w.*cos(n*sigmas.^(-1)*2*pi*5 + (c/2)*(n/sigmas').^2);

x = abs(chirps(:, 15)); % base signal

figure; plot(x); title('bidirectional gaussian chirp signal')

xlabel('Time(s)'); ylabel('Amplitude'); axis tight

%--------------------------------------------------------------

%adding shot noise

y = []; num_itter = 30; % number of itterations

for i = 1:num_itter

% append

y = [y; x];

end

Y = zeros(size(t)); Y(1:length(y)) = y;

figure; plot(t, abs(Y)); title('the final signal') axis tight

%//////////////////////////////////////////////////////////////////////////////////////////////////////

i write another code for generating this chirp gaussian signal but i can add shot noise to it:

clear all; clc

%--------------------------------------------------------------

% chirp signal generation

fs=1e3; t=0:1/fs:1;

f1=0; f2=20;

a=(f2-f1)/(t(end)-t(1)); f=f1+a*t;

x=cos(2*pi*f.*t);

subplot(2,1,1); plot(t,x); title(['down chirp signal']); xlabel('Time(s)'); ylabel('Amplitude');

% gaussian pulse generation

sigma=0.1; t1=-0.5:1/fs:0.5;

variance=sigma^2; w=1/(sqrt(2*pi*variance))*(exp(-t1.^2/(2*variance)));

subplot(2,1,2) plot(t1,w,'b'); title(['Gaussian Pulse \sigma=', num2str(sigma),'s']);

xlabel('Time(s)'); ylabel('Amplitude');

% gaussian chirp pulse generation

figure; xw = w(:) .* x(:);

plot(t,abs(xw)) xlim([0 1])\ xlabel('Time(s)'); ylabel('Amplitude');

title(['gaussian down chirp signal']);

%adding shot noise

y = []; num_itter = 32; % number of itterations

for i = 1:num_itter

% append

y = [y; xw];

end

T=0:1/fs:32.1; Y = zeros(size(T)); Y(1:length(y)) = y;

figure; plot(T,abs( Y));

title('the transmitting signal') xlabel('Time(s)'); ylabel('Amplitude');

axis tight

please help me!!!

thanks,Majid.

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Answer 1

Mathieu NOE 2021-5-16

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/831013-adding-and-generation-of-shot-noise-to-a-gaussian-chirp-signal#answer_700833

在 MATLAB Online 中打开

hello

minor bug fixed in the last lines (see comments ) - it's the time vector definition (length) was incorrect

%--------------------------------------------------------------
% chirp signal generation
fs=1e3;  t=0:1/fs:1; 
f1=0; f2=20;
a=(f2-f1)/(t(end)-t(1));   f=f1+a*t;
x=cos(2*pi*f.*t);
subplot(2,1,1); plot(t,x); title(['down chirp signal']); xlabel('Time(s)'); ylabel('Amplitude');
% gaussian pulse generation
sigma=0.1; t1=-0.5:1/fs:0.5;
variance=sigma^2; w=1/(sqrt(2*pi*variance))*(exp(-t1.^2/(2*variance)));
subplot(2,1,2) ;plot(t1,w,'b'); title(['Gaussian Pulse \sigma=', num2str(sigma),'s']);
xlabel('Time(s)'); ylabel('Amplitude');
% gaussian chirp pulse generation
figure; xw = w(:) .* x(:);
plot(t,abs(xw));
xlim([0 1]); xlabel('Time(s)'); ylabel('Amplitude');
title(['gaussian down chirp signal']);
%adding shot noise
y = [];  num_itter = 32; % number of itterations
for i = 1:num_itter
    % append
    y = [y; xw]; 
end
T=(0:length(y)-1) *1/fs;                    % time axis fixed
% Y = zeros(size(T));  Y(1:length(y)) = y;  % no need for this line 
figure; plot(T,abs(y));
title('the transmitting signal') ;
xlabel('Time(s)'); ylabel('Amplitude');
axis tight

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Mathieu NOE 2021-5-16

在 MATLAB Online 中打开

hello

I found this Fex submission

Shot Noise Simulation - File Exchange - MATLAB Central (mathworks.com)

I slightly modified the code to not use exprnd which requires the Statistics and Machine Learning Toolbox.

% Simulate Shot Noise
% Here we generate a Poisson Impulse Process (a kind of white noise)
clear all; close all; clc
%%
mu = 1; % average wait time between events
N = 50; % number of events along the simulation
t_tick = 1e-3; % time tick for plotting/simulating
% time_between = exprnd(mu, N, 1); % random waiting times between events (exponential pdf)
time_between = -mu*log(rand(N, 1)); % random waiting times between events (exponential pdf)
time = cumsum( time_between ); % actual time of events is the cumulative sum of waiting times
time = round( time/t_tick )*t_tick; % round
time_data1 = [time'; ones(1,N)]'; % a matrix containing event times + '1' per each event
time_data2 = [ (0:t_tick:max(time) )'    zeros( 1+max(time)/t_tick, 1 ) ]; % a matrix containing non-event time ticks + '0' per each time tick. This is used for plotting
time_data3=[time_data1; time_data2]; % concatenate both matrices
time_data4=sortrows(time_data3,1); % sort according to time (column 1)
plot(time_data4(:,1), time_data4(:,2) )
ylim( [-0.1 1.1]); grid
ylabel('Events'); title(['Average=' num2str(1/mu) ' events/second']);
%% Now plot fft of the generated Poisson Impulse Process (white noise)
Y=abs(fft(time_data4(:,2)));
f=0:1/max(time):0.5/t_tick;
figure
plot( f,Y(1:length(f)) )
ylabel('psd'); xlabel('frequency [Hz]'); title('PSD');xlim([-10 500]); ylim([-1 54])