FFTN on 2D distribution

I got a known 2D distrubution of a magnetic field and and the following equations to expand my field with 3D Fourier Series:

and are the amplitudes of the harmonics, and are the phase angles. After some research I found matlab's fftn command. But I dont quite understand how I need to prepare my data and so I can feed it properly to the algorithm and get results for and .

Let's assume I got a 2D-matrix with amplitudes of my magnetic field strength ( and ):

S = rand(10,10)

S = 10×10

0.0774 0.0586 0.1233 0.8253 0.4141 0.3026 0.0886 0.1782 0.8257 0.9804 0.8358 0.5366 0.9505 0.7182 0.9771 0.7725 0.3247 0.0484 0.0352 0.1475 0.3372 0.9373 0.7688 0.6740 0.9309 0.3293 0.9938 0.3643 0.1486 0.8021 0.9284 0.3114 0.5688 0.9209 0.5394 0.2210 0.3374 0.2097 0.7423 0.9325 0.6439 0.4171 0.2081 0.5371 0.6221 0.8705 0.3285 0.2187 0.2559 0.0886 0.5821 0.6240 0.9384 0.6517 0.3809 0.6432 0.6882 0.4982 0.1777 0.0094 0.7878 0.7093 0.8652 0.9309 0.0106 0.4748 0.7695 0.4599 0.5664 0.9333 0.0223 0.6135 0.9721 0.2218 0.9598 0.0652 0.8725 0.6674 0.9581 0.1444 0.9269 0.1790 0.5003 0.2586 0.5871 0.8213 0.7123 0.4241 0.7743 0.1457 0.4185 0.4395 0.3895 0.7202 0.0797 0.7705 0.2463 0.8244 0.3332 0.1039

Since The output Y is the same size as X according to the description, I need to modifiy the matrix first. Is this done via a meshgrid or do I understand something wrong?

Answer 1

[Shubham]

Hi @sbr,

It seems you are trying to perform a 3D Fourier transform on a 2D data matrix using MATLAB's fftn function. Since the original data is 2D, you will need to extend it into a 3D matrix. Here's a how you can achieve this:

• Replicate your 2D matrix along the third dimension to simulate a 3D dataset.
• Apply the fftn function to perform the 3D Fourier transform.

Here's an example in MATLAB:

% Assuming S is your 2D matrix
S = rand(10, 10);

% Extend S to a 3D matrix by replicating it along the third dimension
S3D = repmat(S, [1, 1, 10]); % Creates a 10x10x10 matrix

% Perform 3D FFT
Y = fftn(S3D);

% Y will be a 3D matrix of the same size as S3D

The output Y will be a 3D matrix containing complex numbers that represent the amplitudes and frequency components of your data. While meshgrid is helpful for creating coordinate grids for plotting, it is not required for using fftn.

For more information on fftn, refer to the following documentation link:

https://mathworks.com/help/releases//matlab/ref/fftn.html

Hope this helps.