How can I plot the realizations of a Gaussian signal?

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litt.cuss 2019-3-19

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https://ww2.mathworks.cn/matlabcentral/answers/450947-how-can-i-plot-the-realizations-of-a-gaussian-signal

移动：Adam Danz 2023-2-16

采纳的回答： 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).

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 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 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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Answer 1

Adam Danz 2019-3-19

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https://ww2.mathworks.cn/matlabcentral/answers/450947-how-can-i-plot-the-realizations-of-a-gaussian-signal#answer_366110

编辑：Adam Danz 2020-7-14

在 MATLAB Online 中打开

"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)')