How to simulate a signal with a slow (sinusoidal) drift as experimental input for an app?

I am currently experimenting with an app in which I want to create a function that can stabilize a drifting laser input.

However, if the function doesn't work properly it could damage the laser itself. So as to prevent this from happening, I want to generate some sort of input signal that kind of imitates a laser's frequency. But how do I generate a signal with a bit of noise and a slow drift?

The eventual goal is that that signal is used as input and that my function checks every ~5 seconds whether it is within my threshold input from a given 'stabilization value' and either lowers or increases the laser's input to prevent the drift from going too far of the preferred value.

[Mathieu NOE]

hello

do I understand correctly "some sort of input signal that kind of imitates a laser's frequency"

you mean a pulsating laser ?

for that purpose you can use square (signal) function to create a pulse train

to add some noise you can use rand or randn

to add some drift you simply add a term proportionnal to time (affine or polynomial function of time)

[Ben van Zon]

I mean a CW laser input in THz, where the input imitates the 'natural' drift of said laser with a minor sinusoidal drift.

[Mathieu NOE]

sorry, I am not a laser expert, you may have to give more info's (publication or code ?)

[Ben van Zon]

Oh sorry. In general I would require an input that is in the range of 64455378 MHz which has a slight noise of 10 MHz and it has a slow sinusoidal drift with a maximum amplitude of 30 MHz.

The odd number is because I will later change it to another unit that is easier to work with, which emulates the app I intend to make.

Now the question is, how do I make this signal and use it as an input for a matlab app?

Answer 1

[Mathieu NOE]

hello again

this would be my suggestion

now , we are looking at very high frequencies so I wonder what signal duration you are targeting; you may reach the memory limit very rapidely

clc
clearvars

% demo
%  input that is in the range of 64455378 MHz  
 
f_signal = 64455378*1e6;        % mean freq (Hz)

% slow sinusoidal drift with a maximum amplitude of 30 MHz.
f1_amplitude = 30*1e6;    % frequency amplitude 
f1_mod = 1;              % frequency of modulation

% add a slight noise of 10 MHz (random)
f2_amplitude = 10*1e6;    % frequency amplitude 


%% main code 
Fs = f_signal*5;       % sampling frequency
duration = 1e-12;       % seconds


%%%%%%%%%%%
dt = 1/Fs;
samples = floor(duration*Fs)+1;
t = (0:dt:(samples-1)*dt);
omega = 2*pi*(f_signal+f1_amplitude.*sin(2*pi*f1_mod.*t + 2*f2_amplitude.*(rand(1,samples)-0.5)));

figure(1);
plot(t,omega)

angle_increment = omega.*dt;
angle = cumtrapz(angle_increment);  % angle is the time integral of omega.
signal = sin(angle);

figure(2);
plot(t,signal)