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

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.

[Wayne King]

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?

[Gova ReDDy]

Im using like this freqz2(FT,[32 32]);

Answer 1

[Wayne King]

Didn't I show this already?

rng default;
x = randn(20,20);
xdft2 = fft2(x);
sum(x(:))
xdft2(1,1)

Answer 2

[Wayne King]

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)

Answer 3

[Wayne King]

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)

[Gova ReDDy]

*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]

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]

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.

Answer 4

[Image Analyst]

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.

Answer 5

[Gova ReDDy]

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.

[Walter Roberson]

Frequency is encoded by position, not by value.

[Gova ReDDy]

Position is defined by both the row and cloumn index ,can you please briefly expalin how to get frequency for a particular position.

Answer 6

[umar siyab]

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