Hi Simon,
I understand that you want to perform a spatial fast Fourier transform from a set of x-coordinates, y-coordinates and a value at a particular position using the "fft2" function of MATLAB.
For better performance of the "fft2" function, the data must be interpolated onto a regular grid accurately. The "meshgrid" function of MATLAB can be used to convert coordinates into a grid of points to represent spatial domain and then the "griddata" function of MATLAB can be used to estimate the values at the grid points based on the original data.
Please refer to the example MATLAB code below for more understanding:
% Assuming you have the xcoordinate, ycoordinate, and value vectors
xcoordinate = [-2.024, -2.924, 3.042, 0, 2.412, 1.119];
ycoordinate = [3.043, 2.342, 1.119, -2.293, -1.192, 0];
value = [12, 23, 43, 92, 1, 4];
% Define the grid
xMin = min(xcoordinate);
xMax = max(xcoordinate);
yMin = min(ycoordinate);
yMax = max(ycoordinate);
gridSize = 100; % Adjust the grid size as needed
%using the meshgrid function to create a grid of points
[X, Y] = meshgrid(linspace(xMin, xMax, gridSize), linspace(yMin, yMax, gridSize));
% Interpolate the data using the griddata function
V = griddata(xcoordinate, ycoordinate, value, X, Y, 'nearest');% Experiments can be done using various methods like 'linear', 'cubic' etc.
% Compute the 2D FFT
fft2Data = fft2(V);
% Visualize the frequency spectrum
figure;
imagesc(abs(fftshift(fft2Data)));
colormap jet;
colorbar;
xlabel('Frequency (k_x)');
ylabel('Frequency (k_y)');
title('2D Frequency Spectrum');
The above method will help to obtain better results using the "fft2" function.
To know more about the "meshgrid" and "griddata" functions, please refer to the MATLAB documentation links given below respectively:
- https://www.mathworks.com/help/matlab/ref/meshgrid.html
- https://www.mathworks.com/help/matlab/ref/griddata.html
I hope this helps to resolve the query.
Thanks,
Abhimenyu
