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

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

Answer 1

[Nipun]

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