필터 지우기
필터 지우기

Understanding FFT in MATLAB

조회 수: 3 (최근 30일)
Janee
Janee 2024년 3월 13일
답변: Paul 2024년 3월 13일
I am exploring the differences between fftw in MATLAB and C/C++. I think this maybe a straightforward question but for some reason I don't see it.
Assume the following MATLAB code:
Nx = 8;
Ny = 8;
Lx =16;
%-----------
xi_x = (2*pi)/Lx;
xi = ((0:Nx-1)/Nx)*(2*pi);
x = xi/xi_x;
ylow = 0;
yupp =6;
ygl = cos ( pi * ( 0 : Ny ) / Ny )';
ygl = (1/2)*(((yupp-ylow)*ygl) + (yupp+ylow));
[X,Y] = meshgrid(x,ygl);
%define function u:
u = (Y-ylow) .* (Y-yupp) .* sin( (2*pi / Lx) * X);
uh = fft(u,[],2);
%pad uh with zeros
[Ny Nx]=size(uh);
m=Nx*3/2;
uhp=[uh(:,1:Nx/2) zeros(Ny,(m-Nx)) uh(:,Nx/2+1:Nx)];
%take ifft
up=real(ifft(uhp,[],2));
u1 = real(ifft(uh,[],2)); %same as u
My question above since both ``uh`` and ``uhp`` are the same values with extra zero padding, why is the inverse of fft of these two different? Meaning if ``uh`` is:
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 5.2721i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 5.2721i
-0.0000 + 0.0000i 0.0000 +18.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -18.0000i
-0.0000 + 0.0000i 0.0000 +30.7279i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -30.7279i
-0.0000 + 0.0000i 0.0000 +36.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -36.0000i
-0.0000 + 0.0000i 0.0000 +30.7279i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -30.7279i
-0.0000 + 0.0000i 0.0000 +18.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -18.0000i
0.0000 + 0.0000i 0.0000 + 5.2721i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 5.2721i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
and ``uhp`` is:
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 5.2721i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 5.2721i
-0.0000 + 0.0000i 0.0000 +18.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -18.0000i
-0.0000 + 0.0000i 0.0000 +30.7279i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -30.7279i
-0.0000 + 0.0000i 0.0000 +36.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -36.0000i
-0.0000 + 0.0000i 0.0000 +30.7279i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -30.7279i
-0.0000 + 0.0000i 0.0000 +18.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 -18.0000i
0.0000 + 0.0000i 0.0000 + 5.2721i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 5.2721i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
Then why the `` real(ifft(uh,[],2))`` equals:
0 0 0 0 0 0 0 0
0 -0.9320 -1.3180 -0.9320 -0.0000 0.9320 1.3180 0.9320
-0.0000 -3.1820 -4.5000 -3.1820 -0.0000 3.1820 4.5000 3.1820
0 -5.4320 -7.6820 -5.4320 -0.0000 5.4320 7.6820 5.4320
-0.0000 -6.3640 -9.0000 -6.3640 -0.0000 6.3640 9.0000 6.3640
0 -5.4320 -7.6820 -5.4320 -0.0000 5.4320 7.6820 5.4320
-0.0000 -3.1820 -4.5000 -3.1820 -0.0000 3.1820 4.5000 3.1820
0 -0.9320 -1.3180 -0.9320 -0.0000 0.9320 1.3180 0.9320
0 0 0 0 0 0 0 0
and ``up=ifft(uhp,[],2); `` is:
0 0 0 0 0 0 0 0 0 0 0 0
0 -0.4393 -0.7610 -0.8787 -0.7610 -0.4393 -0.0000 0.4393 0.7610 0.8787 0.7610 0.4393
-0.0000 -1.5000 -2.5981 -3.0000 -2.5981 -1.5000 -0.0000 1.5000 2.5981 3.0000 2.5981 1.5000
0 -2.5607 -4.4352 -5.1213 -4.4352 -2.5607 -0.0000 2.5607 4.4352 5.1213 4.4352 2.5607
-0.0000 -3.0000 -5.1962 -6.0000 -5.1962 -3.0000 -0.0000 3.0000 5.1962 6.0000 5.1962 3.0000
0 -2.5607 -4.4352 -5.1213 -4.4352 -2.5607 -0.0000 2.5607 4.4352 5.1213 4.4352 2.5607
-0.0000 -1.5000 -2.5981 -3.0000 -2.5981 -1.5000 -0.0000 1.5000 2.5981 3.0000 2.5981 1.5000
0 -0.4393 -0.7610 -0.8787 -0.7610 -0.4393 -0.0000 0.4393 0.7610 0.8787 0.7610 0.4393
0 0 0 0 0 0 0 0 0 0 0 0
The reason I ask b/c in C/C++ when padding my arrays similarly and taking the ifft my code returns the same output, so ``real(ifft(uh,[],2))`` = ``real(ifft(uhp,[],2))``

이 질문에 답변하려면 로그인하십시오.

답변 (1개)

Paul
Paul 2024년 3월 13일
Hi Janee,
Speaking only to the Matlab side of this question, why would it expected that the rows of u1 and up be the same? Each row of u1 and up will have a different number of elements. Based that fact alone, how could u1 and up be the same?
I'm suprised with that result in C++.

카테고리

Help Center 및 File Exchange에서 Fourier Analysis and Filtering에 대해 자세히 알아보기

태그

Community Treasure Hunt

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

Start Hunting!

Translated by