[Last Call] Learn about multicloud storage options and how to improve your company's cloud strategy. Register Now

x
?
Solved

2D circular convolution (part 2)

Posted on 2004-11-07
5
Medium Priority
?
853 Views
Last Modified: 2008-01-09
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??
0
Comment
Question by:mte01
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 2
  • 2
5 Comments
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 12517455
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.  
0
 
LVL 31

Expert Comment

by:GwynforWeb
ID: 12517594
......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) )  
0
 
LVL 3

Author Comment

by:mte01
ID: 12518759
>> 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........
0
 

Accepted Solution

by:
ee_ai_construct earned 0 total points
ID: 12664900
The site guidelines prohibit questions exceeding 500 points.

ai, cs admin
0
 
LVL 3

Author Comment

by:mte01
ID: 12665355
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......
0

Featured Post

Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Lithium-ion batteries area cornerstone of today's portable electronic devices, and even though they are relied upon heavily, their chemistry and origin are not of common knowledge. This article is about a device on which every smartphone, laptop, an…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
Suggested Courses

656 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question