Matlab code help - Gaussian Function

[BeeGee]

Hello,

I am new to this forum so please kindly let me know if my question needs to be posted in another area.
I am trying to write a MATLAB code to show a chirped Gaussian function and I am having some trouble with it. I am trying to obtain a chirped Gaussian pulse by modulating a chirped sinusoid by a Gaussian envelope. The modulation frequency is 50GHz.

When I implement the Gaussian code, I don't believe I am getting the right results.

Any help that can be rendered is much appreciated.

My code is below:

c = 3e8*1e-12; % (m/ps; set time unit to ps)

N = 2^16; % Number of time points
tmin = 0; % time aperture (window) start time
tmax = 1e3; % time aperture stop time (ps);
t0 = (tmax-tmin)/2; % center the pulse in the time window (ps)
dt = (tmax - tmin)/(N-1); % time step
t = (tmin:dt:tmax)'; % Time scale

lambda = 1550e-9; % Wavelength of launched pulse (m)
bandwidth = 20e-9; % starting bandwidth (nm)
P0 = 100; % peak power (W)
A = sqrt(P0); % A is the amplitude of the wave to be propagated

T0 = 0.44*lambda^2/(c*bandwidth); % FWHM of Guassian

chirp = -1;
w = 2*pi*50e9;
cp = A*exp(i*w*t).*exp((-(t-t0).^2/2*T0^2)*(1-i*chirp*T0^2)) % Chirped Gaussian function
cpf = fft(cp);

figure;
plot(t(N/2-400:N/2+400), abs(cp(N/2-400:N/2+400)), 'linewidth', 2); %time domain plot
figure;

plot(f, (cpf), 'linewidth', 2); %frequency domain plot

Thank you

 

[BigJDubs]

!</code>Thanks for your help,You need to make a few modifications and additions to your code to get the desired chirped Gaussian pulse. First, you need to generate the frequency axis, which you can do using the <code>fftfreq</code> function. You can add the following line to your code:<code>f = fftfreq(N,dt); % Generate frequency axis</code>Second, you need to adjust the chirp coefficient in your expression for the chirped Gaussian pulse. The chirp coefficient is given by c_chirp = -1/T0^2, where T0 is the temporal width of the Gaussian envelope. So, you need to replace your line:<code>chirp = -1;</code>with<code>chirp = -1/(T0^2);</code>Thirdly, you need to adjust the scaling of the frequency axis. The frequency axis should be scaled such that it corresponds to frequencies in GHz. You can do this by multiplying the frequency axis by an appropriate scaling factor. You can add the following line to your code:<code>f = f*1e-9; % Scale frequency axis to GHz</code>After making these modifications and additions to your code, you should be able to obtain the desired chirped Gaussian pulse.I hope this helps.