CODEWITHSUNDEEP
matlabmatrixconvolution
pap
pap

Reputation: 45

Is there a way to perform column-wise convolution in MATLAB using conv()?

I have two 2D matrices with the same number of columns, A and B. I want to convolve the corresponding columns of these two matrices and store the result into a new one call it result. Assuming that result has the appropriate dimensions, my current approach is something like: 

for i = 1 : size( A, 2 ) % number of columns
    result(:,i) = conv( A(:,i), B(:,i) );
end

Is there a way to avoid this loop using conv() or perhaps conv2() directly?

Upvotes: 1

Views: 980

Answers (2)

Luis Mendo
Luis Mendo

Reputation: 112699

You can use the relationship between (circular) convolution and DFT, and exploit the fact that fft, unlike conv2, can work along a specified dimension: 

A = rand(5,7);
B = rand(4,7); % example matrices. Same number of columns
s = size(A,1)+size(B,1)-1; % number of rows of result
result = ifft(fft(A,s,1).*fft(B,s,1));

Note that due to floating-point numerical precision there may be slight differences, of the order of eps, between this result and that obtained with for and conv. In particular, if your inputs are real the result may have a (very small) imaginary part, so you may want to apply real to the result.

Upvotes: 3

Dr. X
Dr. X

Reputation: 2930

If you want to use conv function you can try conv(A_i,B_i, 'full') but you can also use below code for convolution, e.g. for column convolution convIt(A,B,1) and for row convolution convIt(A,B,2)

function C = convIt(A,B,dim)
% the code is equivalent to running conv(A_i,B_i, 'full') in matlab
% (where A_i and B_i are columns (dim=1) or rows (dim=2) of A,B)
% and then stack the results together

if 1==dim || nargin<3 % default
  A = [A;zeros(size(A))];
  B = [B;zeros(size(B))];
elseif 2==dim
  A = [A,zeros(size(A))];
  B = [B,zeros(size(B))];
end
C = ifft(fft(A,[],dim).*fft(B,[],dim),[],dim);
if 1==dim || nargin<3 % default
  C = C(1:end-1,:);
elseif 2==dim
  C = C(:,1:end-1);
end

Upvotes: 0

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