41 views (last 30 days)
Show older comments
Janee on 6 Aug 2024 at 5:32
Commented: Janee on 7 Aug 2024 at 3:01
Accepted Answer: Matt J
Open in MATLAB Online
I am trying to understand how the FFT of different directions in MATLAB works to reproduce in C/C++ instead.
So far I have the following simple example in MATLAB:
clearvars; clc; close all;
%3D FFT test
Nx = 8;
Ny = 4;
Nz= 6;
Lx =16;
Ly = 6;
dx = Lx/Nx;
dy = Ly/Ny;
%-----------
xi_x = (2*pi)/Lx;
yi_y = (2*pi)/Ly;
xi = ((0:Nx-1)/Nx)*(2*pi);
yi = ((0:Ny-1)/Ny)*(2*pi);
x = xi/xi_x;
y = yi/yi_y;
zlow = 0; %a
zupp =6; %b
Lz = (zupp-zlow);
eta_zgl = 2/Lz;
[D,zgl] = cheb(Nz);
zgl = (1/2)*(((zupp-zlow)*zgl) + (zupp+zlow));
[X,Z,Y] = meshgrid(x,zgl,y); %this gives 3d grid with z-by-x-by-y size (i.e. ZXY)
%ICs
A = 2*pi / Lx;
B = 2*pi / Ly;
u = (Z-zlow) .* (Z-zupp) .* sin(A*X).* sin(B*Y);
uh1 =(fft(u,[],3));%ZXY
uh2 =(fft(u,[],1));%ZXY
uh3 =(fft(u,[],2));%ZXY
So, in C/C++ I have a 3D tensor with (Nz+1) rows and Nx coumns and Ny matrices and taking the 1D FFT along each "row" of u returns the same results as the following in MATLAB:
uh3 =(fft(u,[],2));%ZXY
While taking the 1D FFT of u along each column of u in C/C++ returns the same result as the following in MATLAB:
uh2 =(fft(u,[],1));%ZXY
Then my question is what does this 1D FFT represent? and how should I represent it in C/C++?
uh1 =(fft(u,[],3));%ZXY
The cheb(N) function is:
function [ D, x ] = cheb ( N )
if ( N == 0 )
D = 0.0;
x = 1.0;
return
end
x = cos ( pi * ( 0 : N ) / N )';
c = [ 2.0; ones(N-1,1); 2.0 ] .* (-1.0).^(0:N)';
X = repmat ( x, 1, N + 1 );
dX = X - X';
% Set the off diagonal entries.
D =( c * (1.0 ./ c )' ) ./ ( dX + ( eye ( N + 1 ) ) );
% Diagonal entries.
D = D - diag ( sum ( D' ) );
return
end
0 Comments Show -2 older commentsHide -2 older comments
Show -2 older commentsHide -2 older comments
Sign in to comment.
Sign in to answer this question.
Accepted Answer
Matt J on 6 Aug 2024 at 5:40
Why reinvent the wheel. Why not just use the open source FFTW C/C++ library (which Matlab is based on).
In any case, the mathematical interpretation of Matlab's 1D FFT is in the documentation,
https://www.mathworks.com/help/matlab/ref/fft.html#buuutyt-5
9 Comments Show 7 older commentsHide 7 older comments
Show 7 older commentsHide 7 older comments
Janee on 6 Aug 2024 at 5:44
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230821
I am using the FFTW library in C++ and I have tested Eigen FFT functions as well. FFTW library is not super user-friendly honestly and I have tried to reproduce the FFT MATLAB output to no avail. Thanks.
Matt J on 6 Aug 2024 at 5:50
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230826
Edited: Matt J on 6 Aug 2024 at 5:52
Is the difference more than just a global scaling factor? We cannot assess the problem without examples.
Janee on 6 Aug 2024 at 5:55
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230831
Open in MATLAB Online
There's no difference. It is just that I am not sure what "3" here represents in
uh1 =(fft(u,[],3));%ZXY
Like, I get that it supposed to be along "y" direction, but what does that really mean? for a 3D tensor u with nz+1 rows, nx columns and y matrices what does 1D FFT of u along y mean (i.e. 3)?
Janee on 6 Aug 2024 at 5:56
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230836
As the link you posted explains FFT along each columns is (u,[],1) and FFT along each row is (u,[],2) then what is fft(u,[],3)?
Matt J on 6 Aug 2024 at 5:58
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230841
Edited: Matt J on 6 Aug 2024 at 5:59
Since you understand that fft(u,[],1) and fft(u,[],2) are the same operation (along different dimensions), why do you think there is a different meaning to fft(u,[],3)? There isn't.
Matt J on 6 Aug 2024 at 6:02
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230846
Edited: Matt J on 6 Aug 2024 at 6:02
Open in MATLAB Online
It is the same as if you did it in 3 steps:
tmp=shiftdim(u,2);
Tmp=fft(tmp,[],1);
uh3=shiftdim( Tmp , -2);
Janee on 6 Aug 2024 at 6:04
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230851
So, fft(u,[],3) is just 1D fft along each row of u?
Matt J on 6 Aug 2024 at 7:40
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3230906
Edited: Matt J on 7 Aug 2024 at 0:40
No, it is the fft along each vector u(i,j,:).
Janee on 7 Aug 2024 at 3:01
Direct link to this comment
https://www.mathworks.com/matlabcentral/answers/2143236-fft-of-3d-array-in-matlab#comment_3231654
This line "fft along each u(i,j,:)" actually solves my issue and makes more sense!
Sign in to comment.
More Answers (0)
Sign in to answer this question.
See Also
Categories
MATLABMathematicsFourier Analysis and Filtering
Find more on Fourier Analysis and Filtering in Help Center and File Exchange
Tags
- meshgrid
- fft
- numerical libraries
- c/c++
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!
An Error Occurred
Unable to complete the action because of changes made to the page. Reload the page to see its updated state.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- Deutsch
- English
- Français
- United Kingdom(English)
Asia Pacific
- Australia (English)
- India (English)
- New Zealand (English)
- 中国
- 日本Japanese (日本語)
- 한국Korean (한국어)
Contact your local office
