# how to deconvolute a array ?

18 vues (au cours des 30 derniers jours)
Rabih Sokhen le 8 Fév 2022
Commenté : Chris Turnes le 11 Fév 2022
hy guys
i would like to deconvolute a matrix
code:
clear all
clc
a=rand(10,3);
b=rand10,3); %b=conv2(a,c)
%suppose that b is already the convolution of the array "a" with an array "c"
% I would like to deconvulte " b " to re-obtain "a" and "c".
% any idea how to do so?
##### 0 commentairesAfficher -2 commentaires plus anciensMasquer -2 commentaires plus anciens

Connectez-vous pour commenter.

### Réponse acceptée

Chris Turnes le 9 Fév 2022
Deconvolution is equivalent to polynomial division. You can get the polynomial division and its remainder with the deconv function.
rng('default');
% Take two vectors.
a = randn(7,1);
c = randn(10,1);
% Compute their convolution.
b = conv(a, c);
% "Recover" the first by deconvolving c from b:
[ahat,r] = deconv(b, c);
% Check the residual and the remainder polynomial
norm(a-ahat)
ans = 8.1907e-11
r'
ans = 1×16
1.0e+-9 * 0 0 0 0 0 0 0 0.2664 0.2397 -0.1352 0.2409 0.0603 -0.0114 0.0599 -0.0156 -0.0101
However, it's important to note that this is not a least-squares solution to the deconvolution, and if b isn't really the result convolving something with c, you may not get an answer that's particularly close to the least squares result. To get the least squares result, you would construct the Toeplitz system corresponding to the convolution and solve it:
% Add some "noise" to c:
bhat = conv(a, c + 1e-3*randn(size(c)));
% Solve with deconv:
ahat_deconv = deconv(bhat, c);
% Compare convolving the result with c against the vector we started with:
norm(bhat - conv(ahat_deconv, c))
ans = 6.0224e+03
% Solve with least-squares:
T = convmtx(c, length(a));
ahat_ls = T \ bhat;
% Compare convolving the least-squares result with c against the vector we
% started with:
norm(bhat - conv(ahat_ls, c))
ans = 0.0044
There are efficient algorithms to solve the Toeplitz system, though there are not any functions directly in MATLAB to do so.
##### 8 commentairesAfficher 6 commentaires plus anciensMasquer 6 commentaires plus anciens
Rabih Sokhen le 11 Fév 2022
clear all
clc
a = randn(5, 7);
c = randn(13,17);
b= full(convmtx2(a, size(a)) \ c(:));
b= reshape(b, size(c)-size(a)+1);
%i tried the following code but i got a error, can you plz help me fix it?
Chris Turnes le 11 Fév 2022
Your error here is that you're not specifying the right size for the convolution matrix. The size argument is the size of the thing you are convolving with a -- so in this case, the size of b. You've alredy determined this later, so you just need to pass it into the function:
a = randn(5, 7);
c = randn(13,17);
szB = size(c) - size(a) + 1;
b= full(convmtx2(a, szB) \ c(:));
b= reshape(b, szB);

Connectez-vous pour commenter.

### Catégories

En savoir plus sur Discrete Math dans Help Center et File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by