FFT result looks nothing like analytic result

2 次查看（过去 30 天）
James Kirk
James Kirk 2015-11-29
编辑： Rick Rosson 2016-3-14
Forgive me if I am missing understanding something simple here but I am confused by exactly what the FFT function returns in Matlab. I have code to compare the result of FFT to the analytic result of the fourier transform of a gaussian:
steps = 2^10; lim = 4;
x = linspace(-lim, lim, steps);
w = lim/4; A = 1;
func = A*exp((-1).*(x./w).^2); % Gaussian
Analytic = sqrt(pi)*w*exp(-(w*pi.*x).^2); % Analytic Transform
Func = fftshift(fft(func)); % FFT transform
When I plot this, the fft function looks nothing like the analytic result:
If anyone could shed some light on why this is and how I can adapt my use of the FFT function to give me back the analytic result I would greatly appreciate it!
I am asking this question as I have been developing some code to model the propagation of various beams through a turbulent medium using phase screens. For the code to be valid it is important that the Fourier Transforms produced agree with Physics.

请先登录，再回答此问题。

回答（1 个）

Rick Rosson
Rick Rosson 2016-1-6
编辑：Rick Rosson 2016-3-14
steps = 2^10; lim = 4;
dx = 2*lim/steps;
x = -lim:dx:lim-dx;
% x = linspace(-lim, lim, steps);
Fs = 1/dx;
dF = Fs/steps;
f = -Fs/2:dF:Fs/2-dF;
w = lim/4; A = 1;
func = A*exp((-1).*(x./w).^2); % Gaussian
% Analytic = sqrt(pi)*w*exp(-(w*pi.*x).^2); % Analytic Transform
Analytic = sqrt(pi)*w*exp(-(w*pi.*f).^2);
% Func = fftshift(fft(func)); % FFT transform
Func = dx*fftshift(fft(ifftshift(func))); % FFT transform
diff = abs(Func) - Analytic;
figure;
subplot(2,1,1);
plot(f,abs(Func),f,Analytic);
xlim([-4 4]);
subplot(2,1,2);
plot(f,diff);
xlim([-4 4]);
  2 个评论
Luna
Luna 2016-2-29
编辑：Luna 2016-2-29
Dear Rick,
I have troubles with exactly the same problem. I just tested your code and it produces, as in James example, an output fft function that do not agree with the analytical one. Can you explain why? Is there a reason? Thank you very much
Luna

请先登录，再进行评论。

类别

在 Help Center 和 File Exchange 中查找有关 Fourier Analysis and Filtering 的更多信息

标签

产品

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by