Sub sampling in frequency domain

Hi,

I like to know the procedure to subsample an image in frequency domain

For example
Image =
                      121	122	131	141
	     123	132          141	152
                      101     97           191            120
                     100      41            40               78

Sub sampled image is average of 2X2 sub matrix without overlap

Result
------------
Sub sampled image =

                124.5	   141.25
               84.75           107.25


The procedure
1.	I have converted Image into frequency domain using Fast Fourier
transform
2.	Subsample in frequency domain (I like to know this part, pls help
out to solve this problem)
3.	Convert it to time domain , I like get result as I shown above

I really appreciate if you refer me any website which gives detailed
study of sub sampling in Fourier  domain

saravanan wrote:
> Hi,
>
> I like to know the procedure to subsample an image in frequency domain
>
> For example
> Image =
>                      121 122 131 141
>      123 132          141 152
>                      101     97           191            120
>                     100      41            40               78
>
> Sub sampled image is average of 2X2 sub matrix without overlap
>
> Result
> ------------
> Sub sampled image =
>
>                124.5    141.25
>               84.75           107.25
>
>
> The procedure
> 1. I have converted Image into frequency domain using Fast Fourier
> transform
> 2. Subsample in frequency domain (I like to know this part, pls help
> out to solve this problem)
> 3. Convert it to time domain , I like get result as I shown above
>
> I really appreciate if you refer me any website which gives detailed
> study of sub sampling in Fourier  domain

Subsampling or downsampling is well treated in comp.dsp, dspguru, etc.

Most of what you'll find is for 1-D but the principles are the same:

1) Lowpass filter the data to avoid aliasing - so in your case this would be 
"lowpass" in the spatial domain or convolution in the frequency domain with 
a 2-D sinc-like function.  A type of localized averaging...

2) Reduce the sample rate in frequency after having done the filtering.

Some methods will be better than others for your purposes.  Also check 
sci.image.processing.  Sometimes practical image processing skips steps that 
signal processing folks would want to use.

Fred