Finding the below fft

I have the fft result with which I need to perform the spatial frequency distribution in (um)-1 units and plot the spatial frequency spectrum for y=0.01,0.02,0.03,1. I need some idea how to proceed with that?

Answer 1

[William Rose]

@Amy Topaz,

[edited: correct typos, not in the code]

You are using the 2D FFT. The 2D FFT is appropriate for images or other 2D data in which there is a uniform grid spacing along the two independent variables. In this case, there are only 4 y-values, and they are unevenly spaced. Therefore I recommend doing the 1D FFT on the array Hy. This will compute the 1D FFT of each column of Hy. Since x varies along the rows of Hy, I take the FFT of the transpose of Hy. fft(Hy') returns a complex array whose columns are the FFTs of the rows of Hy. The absolute values of the complex numbers are the magnitudes of the Fourier transform.

%AmyTopazscript.m, modified by WCR, 2022-03-28
clear;
g = 1e-7;
dx=0.01;
x = -0.5:dx:0.5;
N=length(x);
df=1/(N*dx);    %frequency interval for the FT
f=(0:N-1)*df;   %frequency vector for the FT
y = [0.01*g 0.2*g 0.6*g  g]';
Hy = (-1/2*pi)*(log((g/2 + x).^2 + (y).^2./(g/2 - x).^2 + (y).^2));
Z = fft(Hy');
%Plot results
figure;
subplot(211)
plot(x,Hy(1,:),'-k',x,Hy(2,:),'-r',x,Hy(3,:),'-g',x,Hy(4,:),'-b');
grid on; xlabel('x (\mum)'); ylabel('Hy(x)');
legend('0.01g','0.2g','0.6g','g');
subplot(212)
plot(f,abs(Z(:,1)),'-k',f,abs(Z(:,2)),'-r',f,abs(Z(:,3)),'-g',f,abs(Z(:,4)),'-b');
grid on; xlabel('Spatial frequency (\mum^-^1)'); ylabel('|FT(Hy)|');
xlim([0 N*df/2]);       %plot FT up to Nyquist frequency
legend('0.01g','0.2g','0.6g','g');

Try the code above.