How to write a function which performs deconvolution to solve for x given y and h where y = h*x (all column vectors) using linsolve

3 次查看(过去 30 天)
I do know that the deconv() function can do it perfectly. However, I was wondering if anyone can write a function with linsolve() to perform deconvolution. I have tried to make a simple implementation but it seems to be not universal.
function x = mdeconv(h, y)
%Deconvolution
%
hT = toeplitz([h(1) zeros(1,length(y)-length(h))], [h zeros(1,length(y)-length(h)) ]);
%x = linsolve(hT, y);
x = y/hT;
end

回答(1 个)

Nipun
Nipun 2024-5-23
Hi William,
I understand that you are trying to perform deconvolution using the linsolve function instead of the deconv function in MATLAB. Below is a modified version of your function to use linsolve for deconvolution:
function x = mdeconv(h, y)
% Deconvolution using linsolve
%
% Inputs:
% h - Impulse response
% y - Convolved signal
%
% Output:
% x - Deconvolved signal
% Create the Toeplitz matrix for h
hT = toeplitz([h(:); zeros(length(y)-length(h), 1)], [h(1), zeros(1, length(y)-1)]);
% Solve for x using linsolve
x = linsolve(hT, y(:));
% Ensure the result is a row vector if y was a row vector
if isrow(y)
x = x.';
end
end
Refer to the following MathWorks documentation for more information on creating Toeplitz matrix in MATLAB: https://in.mathworks.com/help/matlab/ref/toeplitz.html#d126e1740357
Hope this helps.
Regards,
Nipun

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