fft2 - how does it work

Hello, I am trying to understand how fft2 works and what it really means by simple example - my image is black&white stripes:

n = 256;
step = 4;
m_in = zeros(n,n);
for i = 1 : step : n
    m_in(:,i) = 1;
end

I've noticed that if my step is power of 2 then

imshow(abs(fftshift(fft(m_in))))

will provide a black image with step number of white dots (4 in the above example).

Why is that?

Also, if my step in NOT power of 2 (for example step=7), then

imshow(abs(fftshift(fft(m_in))))

will result in simply a full white line accross the entire pic (like in the image below):

Why is that?

Answer 1

[Honglei Chen]

I'm a bit confused by your question, there is no fft2 in your code. All you do is fft along columns. Also for your code, if I change step to 7, I also get a series white dots, which is expected. I don't get that white line.

[moose]

Thank you Chen. Can you explain please why for step=7 series of 7 white dots is expected?

Also, I use the following code and get a straight white line:

n = 256;
step = 7;

m_in = zeros(n,n);

for i = 1 : step : n
    m_in(:,i) = 1;
end

u = fftshift(fft2(m_in));

imshow(abs(u));

can you post your code please? am I missing something?

[Honglei Chen]

This time your code is using fft2 instead of fft. Before, you set every 7th column to all 1's, so the fft of that is an impulse. That's why you'll see white dots at every 7th column.

[moose]

Thanks again Chen. But my question remains - why in the above code, when my step is a power of 2 (4,8,16, etc...), I receive a series of dots (4,8,16 dots, respectively)... while if my step is NOT a power of 2 (7,9, etc...), I get a straight line?