2D circular convolution (part 2)

Two 2D sequences, one is 3 x 4 points & the other is 4 x 3 points in extent, are circularly convolved using (6 x 6)-point 2-D DFTs (Discrete Fourier Transforms). Which samples of the (6 x 6)-output array are identical to the samples of the linear convolution of the two input arrays & which are different??
Who is Participating?
I wear a lot of hats...

"The solutions and answers provided on Experts Exchange have been extremely helpful to me over the last few years. I wear a lot of hats - Developer, Database Administrator, Help Desk, etc., so I know a lot of things but not a lot about one thing. Experts Exchange gives me answers from people who do know a lot about one thing, in a easy to use platform." -Todd S.

I do not entirely follow the question.  Given A=3 by 4  and B=4 by 3   I can see that the convolution is  A**B = 6 by 6  but I do not understand  this statement
      "are circularly convolved using (6 x 6)-point 2-D DFTs (Discrete Fourier Transforms)"
do you mean convolving A and B but taking thier DFT multiplying and then doing an inverse DFT ?   If you you do then the outputs are the same as A**B for all inputs A,B  because of the convolution theorem.  
......see http://mathworld.wolfram.com/ConvolutionTheorem.html  at bottom of page eqn 7, it applies in discrete domain as well.

ie         f**g = F^(-1)( F(f)F(g) )  
mte01Author Commented:
>> are circularly convolved using (6 x 6)-point 2-D DFTs

I mean by that zeros are padded to each input (A & B) before making the circular convolution (i.e. before taking the DFTs of A & B and multiplying them, and then taking the IDFT of the product)

>> then the outputs are the same as A**B for all inputs A,B  because of the convolution theorem

Yes you are right (I checked it out), for any inputs A & B of the specifications above, the circular convolution & the linear convolution are the same (if the DFT is applied on a 6x6 basis - after padding zeros). However, 2D circular convolution (part 1) wouldn't have the same answer........
The site guidelines prohibit questions exceeding 500 points.

ai, cs admin

Experts Exchange Solution brought to you by

Your issues matter to us.

Facing a tech roadblock? Get the help and guidance you need from experienced professionals who care. Ask your question anytime, anywhere, with no hassle.

Start your 7-day free trial
mte01Author Commented:
No sorry....this time it's different....please do read the question, these are two completely different questions!!!!!
Each have a separate answer, and could have been answered by a different expert......
It's more than this solution.Get answers and train to solve all your tech problems - anytime, anywhere.Try it for free Edge Out The Competitionfor your dream job with proven skills and certifications.Get started today Stand Outas the employee with proven skills.Start learning today for free Move Your Career Forwardwith certification training in the latest technologies.Start your trial today
Math / Science

From novice to tech pro — start learning today.

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.