Continue to Site

Welcome to EDAboard.com

Welcome to our site! EDAboard.com is an international Electronics Discussion Forum focused on EDA software, circuits, schematics, books, theory, papers, asic, pld, 8051, DSP, Network, RF, Analog Design, PCB, Service Manuals... and a whole lot more! To participate you need to register. Registration is free. Click here to register now.

Register Log in

[SOLVED] Determine matrices for convolution output

Status
Not open for further replies.
G

gopalgj

Newbie level 4
Joined
Sep 4, 2010
Messages
5
Helped
0
Reputation
0
Reaction score
0
Trophy points
1,281
Activity points
1,319
Hello all,

Consider a 9x9 matrix (M). We can express it as a convolution of two 5x5 matrices (M1, M2) i.e

M = conv2(M1, M2);

Given a matrix M, how can we find M1 & M2?

If one of them can be determined then the other can be computed by known deconvolution algorithms. But, how do we begin with determining the first matrix?

Thanks.
 

in general, it's impossible even for 1x1 matrix :)
 
Why is it impossible to determine the matrices?

For 1x1, convolution is just a simple multiplication:

a * b = c or

a x b = c

b = c/a.

Given "c", we can choose any non-zero for value for "a", and compute "b".
 

yes, that's exactly the point: you have to choose "a", you can't determine "a" from "c", you have degrees of freedom here.
 

I'm trying to find if there is always a solution (M1, M2 exists) or if there is any defined steps instead of trial-n-error.

I wrote down the equation for convolving 2x2 matrices, we get 9 equations (output is 3x3 known matrix) in 8 unknowns (2x2 M1, 2x2 M2). I think its a over-determined system.
 

Status
Not open for further replies.

Similar threads

Part and Inventory Search

Welcome to EDABoard.com

Sponsor

Back
Top