How to calculate and sketch the Fourier Transform of a gaussian function?

Question

Nathan 2022-9-22

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1809830-how-to-calculate-and-sketch-the-fourier-transform-of-a-gaussian-function

评论： Paul 2022-9-22

采纳的回答： Paul

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Hello,

I have the following function:

(exp(-pi.*x.^2) + 0.25.*exp((-pi.*x.^2)/16))
Unrecognized function or variable 'x'.

I'm trying to calculate and sketch its fourier transform version.

This is what I tried but it seems wrong.

x_fit_func = @(x)  (exp(-pi.*x.^2) + 0.25.*exp((-pi.*x.^2)/16));
x = linspace(-10, 10, 50);
x_F = fft(x_fit_func(x))/numel(x);
Fs = 1/mean(diff(x));
Fn = Fs/2;
Fv = linspace(-1, 1, numel(x_F))*Fn;
Iv = 1:numel(Fv);
figure
plot(Fv, fftshift(abs(x_F)))
grid

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Answer 1

Paul 2022-9-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1809830-how-to-calculate-and-sketch-the-fourier-transform-of-a-gaussian-function#answer_1058450

在 MATLAB Online 中打开

Hi Steven

What doesn't seem correct? The only issue I see is the calculation of Fv, modified below.

x_fit_func = @(x) (exp(-pi.*x.^2) + 0.25.*exp((-pi.*x.^2)/16));

x = linspace(-10, 10, 50);

x_F = fft(x_fit_func(x))/numel(x);

Fs = 1/mean(diff(x));

Fv = (-25:24)/50*Fs; % frequency vector for N = 50 (N is even)

figure

plot(Fv, fftshift(abs(x_F)))

grid

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Nathan 2022-9-22

I'm still new to matlab and read this code from another forum, which is why I'm not so sure if the impulse response looks correct. I initially tried fft(f_x) where f_x is my function in time domain but the graph came out looking very weird. Do you mind explain your code briefly? Thank you!