# Image processing problem

1. Dec 23, 2011

### mr_k

hi!
i need help with problem:
Let F(u,v) be the Fourier transform of an M x N image f(x,y). Let g(x,y) be an image of dimensions (2 M) x (2 N) whose Fourier transform G(u,v) is defined as follows:

What does the image g(x,y) look like in terms of f(x,y)?

my solution : g(x,y)=0.25f(x/2,y/2).

Is that true?

thanks :)

2. Dec 23, 2011

### marcusl

No, you're on the wrong track. You have an image that has looks basically the same but has twice (in this case) as many points. These extra points are interpolated between the points of the original f. This is known as zero-padding. See if you can work it out from the DFT expressions.

3. Dec 23, 2011

### AlephZero

You are not completely on the wrong track, but your math solution is wrong, because the functions f(x,y) etc are only defined when x and y are integers. You can't talk about "half a pixel", so f(x/2, y/2) doesn't mean anything if x or y are odd numbers.

On the other hand if you say what your formula means "in words" rather than as a math formula, it does describe what the image "looks like".

4. Dec 24, 2011

### mr_k

Last edited by a moderator: May 5, 2017
5. Dec 24, 2011

### I like Serena

But what happens if x or y is odd?

6. Dec 24, 2011

### mr_k

7. Dec 24, 2011

### I like Serena

Your answer is right, but you should add that if x or y is odd, that the value is effectively interpolated.

8. Dec 24, 2011

thanks!!