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

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majid
majid 2021-5-15
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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回答（1 个）

Mathieu NOE
Mathieu NOE 2021-5-16
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
Mathieu NOE 2021-5-16
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])
maybe you can add this portion of code to yours

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