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How to embed a series of Gaussians in a Lorentzian just by adding functions?

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Hey,
I want to have the shown function in Matlab and use it in my simulations and codes. It is a series of Gaussians (which has a narrow band of around 200 MHz) embedded in a broadband Lorentzian function (approximately 50 GHz). Could you please help me with how I can write a function just by adding some functions to show this figure? I know how to do that by, for example, removing some elements from the Lorentzian at that point and using concatenation techniques. But I need to show this function in my code as the sum or subtraction of some functions because I want to do other processes on it. I have attached a zoom-out figure which shows what I mean as a whole. Then in other pictures with numbers, I mostly want to say I need to define these series of Gaussians embedded into a broader Lorentzian in a flexible way such that I can obtain figures 1, 2, and 3 by changing some parameters of the added functions.
Your help is so much appreciated!

Risposte (1)

Rangesh
Rangesh il 8 Nov 2023
Hi Shaily,
I understand that you would like to embed a series of Gaussian curves into a Lorentzian curve. The provided code accomplishes this task.
x = -100:0.1:100; % Define the x-axis range
% Define the parameters for the Gaussians and Lorentzian
gaussians = {[1, 0, 10], [0.5, -40, 1], [0.8, -50, 8],[0.6,-30,5]};
lorentzian = [1, 0, 50];
% Call the function to evaluate the function values
y = gaussiansInLorentzian(x, gaussians, lorentzian);
% Plot the resulting function
plot(x, y);
In the above code, the range of the x-axis is defined as -100 to 100.The parameters for the Gaussians and the Lorentzian are specified. The function gaussiansInLorentzian is called to evaluate the function values. The resulting function is plotted.
function y = gaussiansInLorentzian(x, gaussians, lorentzian)
% x: Input vector
% gaussians: Cell array of Gaussian parameters [amplitude, mean, standard deviation]
% lorentzian: Lorentzian parameters [amplitude, center, width]
% Initialize the output vector
y = zeros(size(x));
% Evaluate each Gaussian component
for i = 1:numel(gaussians)
gaussian = gaussians{i};
y = y + gaussian(1) * exp(-(x - gaussian(2)).^2 / (2 * gaussian(3)^2));
end
% Evaluate the Lorentzian component
y = y + lorentzian(1) ./ ((x - lorentzian(2)).^2 + (lorentzian(3)/2)^2);
end
The gaussiansInLorentzian function takes the input vector x, a cell array of Gaussian parameters gaussians, and Lorentzian parameters lorentzian. It initializes the output vector y and then evaluates each Gaussian component through iteration. The Gaussian components are added to y and later, the Lorentzian component is evaluated and added to y.
You can modify the code according to your requirements, such as changing the range of the x-axis or adjusting the parameters for the Gaussians and the Lorentzian.
I hope this resolves your query.
With regards,
Rangesh.

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