How can I plot the realizations of a Gaussian signal?

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litt.cuss
litt.cuss 2019-3-19
移动：Adam Danz 2023-2-16
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?
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litt.cuss
litt.cuss 2019-3-21
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
navid seif 2023-2-16
移动：Adam Danz 2023-2-16
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?

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Adam Danz
Adam Danz 2019-3-19
编辑：Adam Danz 2020-7-14
"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)')

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