peak value at the centre of F(0,0) in magnitude plot of fourier transform

2011 11 16
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According to this doc
http://www.mathworks.in/help/toolbox/images/f21-17064.html
My image in this link <http://tinypic.com/view.php?pic=qpgweq&s=5>
consists of a single line when Im using this
FT=fft2(linkImage);
freqz(linkImage)
my output image is <http://tinypic.com/view.php?pic=j5eex1&s=5>
In the doc it is mentioned that the center at F(0,0)of fourier tarnsform contains sum of all values in FT.But in my image along with the centre peak two more peaks are visible.Can someone explain what are they.

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Wayne King
Wayne King 2011-11-16
Hi, I don't see how you are calling freqz() on an image.
freqz() expects two input vectors, or is this not a MATHWORKS' freqz?

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Wayne King
Wayne King 2011-11-22

0 个投票

Didn't I show this already?
rng default;
x = randn(20,20);
xdft2 = fft2(x);
sum(x(:))
xdft2(1,1)

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Wayne King
Wayne King 2011-11-16

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At any rate, I think only when you shift the 2-D Fourier transform does it end up in the middle. Note that:
rng default;
x = randn(20,20);
xdft2 = fft2(x);
sum(x(:))
xdft2(1,1)
Now
xdft2 = fftshift(xdft2);
xdft2(11,11)
Wayne King
Wayne King 2011-11-17

0 个投票

You wrote freqz() above. freqz2() is for a filter.
For example:
h = 0.01*ones(10,10);
sum(h(:))
H = freqz2(h,10,10);
H(6,6)

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Gova ReDDy
Gova ReDDy 2011-11-17
*freqz and freqz2* will give the 1D and 2D frequency response respectively.Can we use both for frequency responses or is there any difference between them.
Wayne King
Wayne King 2011-11-17
freqz2() is for a 2-D FIR filter, freqz() handles both FIR and IIR filters. You can infer the frequency response for your 2-D FIR filter from the 1-D response with freqz() iff your 2-D FIR filter is separable, but I wouldn't assume that this always the case.
Gova ReDDy
Gova ReDDy 2011-11-22
After
Ft=fft2(ximage);
does the frequency value in the First row first coulmn in Ft array will contain sum of all values in ximage or not?
because after fftshift the center frequency will contain the sum of all values in an image.

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Image Analyst
Image Analyst 2011-11-22

0 个投票

Come on, obviously "F(0,0)of Fourier transform contains sum of all values in FT" is NOT CORRECT. It simply can't be (unless your FT is a delta function) - just think about it for half a second. The F(0,0) element is the "DC component" as it is often called and is proportional to the mean of the spatial domain image. Go back and read the documentation and you'll see that it really says "Note that F(0,0) is the sum of all the values of f(m,n)." Note that f is the spatial domain image, not the Fourier Transform! The sum of all the values of the image is, of course, proportional to the mean of the image.
Gova ReDDy
Gova ReDDy 2011-11-23

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After doing Fourier transform of a image I was able to get complex values like 3.3334+i0.2345.
The realpart 3.3334 is magnitude and imaginary part 0.2345 is phase. Does this complex value itself the frequency or is there any method to caluculate the frequency of this complex value.

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Walter Roberson
Walter Roberson 2011-11-23
Frequency is encoded by position, not by value.
Gova ReDDy
Gova ReDDy 2011-11-23
Position is defined by both the row and cloumn index ,can you please briefly expalin how to get frequency for a particular position.

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umar siyab
umar siyab 2011-11-24

0 个投票

when u want to centre the image u must use the fftshift function afterall your image will center at f(0,0)... the f(0,0) will contain the lowest values of pixel as compared to move from centre

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