generate 2d gaussian that exponentially decays over time in matlab

To generate a 2D Gaussian that exponentially decays over time in MATLAB, you can follow these steps:

1. Define the size of the Gaussian matrix. Let's assume you want to generate a 2D Gaussian with a size of 100x100 pixels.

main.m
size = 100;
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2. Create a meshgrid that represents the x and y coordinates of each pixel in the Gaussian matrix.

main.m
[x, y] = meshgrid(-(size/2):(size/2)-1, -(size/2):(size/2)-1);
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3. Define the parameters of your Gaussian, such as the mean, standard deviation, and exponential decay rate.

main.m
mean = [0, 0]; % Replace with your desired mean point
std_dev = 10; % Replace with your desired standard deviation
decay_rate = 0.1; % Replace with your desired decay rate
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4. Calculate the Gaussian values based on the formula:

main.m
gaussian = exp(-decay_rate.*sqrt(x.^2 + y.^2)).*exp(-((x-mean(1)).^2 + (y-mean(2)).^2)/(2*std_dev^2));
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The first term in the equation represents the exponential decay over time, while the second term represents the normal distribution of the Gaussian.

5. Plot the Gaussian using the surf function.

main.m
surf(x, y, gaussian);
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You can adjust the parameters in steps 3 and 4 to achieve the desired decay rate and shape of the Gaussian.

I hope this helps!