How can I plot the realizations of a Gaussian signal?

I would like to plot the realizations of a simple Gaussian signal with mean 0 and unit variance. Let's call it X(t).

If I use the function randn(), I get a vector of gaussian variables, that is for every ω I get a random variable . But what I want is a function of time, that is, fixed ω, I want to see X(t) on my plot.

How can I get that?

[KALYAN ACHARJYA]

What you have tried so far, please show the code?

Can you show in Pictorial representation (diagram), what exactly you are looking for?

[litt.cuss]

I don't have any code because actually I don't know where to start :-(

I thought about a sinusoidal function to show these realizations, or something similar, but my signal is not periodic. Maybe is there another function that can simulate the realizations of the process?

[Adam Danz]

I provided an answer that addreses your first sentence but I'm not sure it completely addresses the rest of your question. Let me know if I can be of further help.

[litt.cuss]

Thank you a lot for your help! I was wondering if there is a generic function, something like a test function, to simulate and plot the trajectories of a Gaussian process, when ω is fixed and the process depends only on time. But I think it always depends on the particular kind of process.

Thank you anyway!

[navid seif]

If s(t) is a guassian signal, then the jth column of Ψi corresponds to πj that πj is a 3D vector [xj; yj; zj] shown above:

How can I implement this formula in MATLAB?

Answer 1

[Adam Danz]

"I would like to plot the realizations of a simple Gaussian signal with mean 0 and unit variance. Let's call it X(t)."

The parameterized equation for a gaussian is below where

• 'a' specifies the amplitude
• 'b' specifies the x-coordinate of the center
• 'c' specifies the width
• 'x' is a vector of x inputs

Note that you could also use gaussmf() if you have the Fuzzy Logic Toolbox.

Also see this answer which includes a vertical offset term and compares the results to gaussmf.

gauss = @(x,a,b,c) a*exp(-(((x-b).^2)/(2*c.^2)));

% demo
x = -4:.01:4;   
amp = 1; 
cnt = 0; 
sig = 1; 
y = gauss(x, amp, cnt, sig);  %same as y = gaussmf(x, [sig, cnt]) * amp; 

figure
plot(x,y)
hold on
plot([cnt,cnt], ylim, ':k') %show center
xlabel('time(ms)')