Complex number and fft
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So I noticed during processing some images in matlab, that the angle phase images after fft+ifft are not the same as the original anymore. When looking at the matrix, I saw that Matlab stores values sometimes as "0", sometimes as "0.000000000000000 + 0.000000000000000i". I was wondering, what is the difference? Isn´t the whole matrix supposed to contain complex numbers?
I also tried a simpler example myself
V = [0, 2];
W = [0, 2+3i, 5, 0, 3+1i];
fft_V = fft(V);
fft_W = fft(W);
vv = ifft(fft_V);
fs_V = fftshift(fft(V));
vvv = ifft(ifftshift(fs_V));
ww = ifft(fft_W);
fs_W = fftshift(fft_W);
www = ifft(ifftshift(fs_W));
w2 = ifft(fft(ww));
While for V everything is normal, 2 things about W make me wonder:
"www" is the same as W, but why are the signs in front of the "0"s inverted? (from + to -)
If one checks "w2 == ww", Matlab returns: "[0 1 1 1 1]", which seems weird. All 5 values are the same, but somehow, the first entry of the vector returns false?
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David Goodmanson
2020-7-25
编辑:David Goodmanson
2020-7-25
Hi Nmak,
you are just getting into standard numerical precision issues. The fft and ifft involove complex variable calculations. Getting things to agree in double precision after a bunch of such calculations doesn't always work exactly. For example
ww(2:end)-w2(2:end)
ans =
0 0 0 0
These elements are truly equal.
w(1)-w2(1)
ans =
0 + 8.8818e-17i
not quite equal. Hence the results of the ww==w2 test.
Sometimes what you see is the result of formatting,
>> W(1)
ans =
0
>> format long
>> W
W =
Columns 1 through 2
0.000000000000000 + 0.000000000000000i 2.000000000000000 + 3.000000000000000i
Columns 3 through 4
5.000000000000000 + 0.000000000000000i 0.000000000000000 + 0.000000000000000i
Column 5
3.000000000000000 + 1.000000000000000i
W(1) is still 0 of course, but since the some of the other elements of W are complex, W(1) is listed in a 0 + 0i format.
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David Goodmanson
2020-7-25
When you have a complex array, then two memory location are allocated for each element, whether that element has a a nonzero imaginary part or not. So:
A = 0:4
W = [0, 2+3i, 5, 0, 3+1i];
whos A W
Name Size Bytes Class Attributes
A 1x5 40 double
W 1x5 80 double complex
At eight bytes per real number for double precision, you can see two real numbers allocated for each element of W. Looking just at a single real element of W,
W(1)
ans = 0
there is no need to report out a zero imaginary part.
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