Calculating cross-correlation using Walsh-Hadamard transform I am trying to implement MLS method of measuring impulse responses. There is an article describing the method: http://www.commsp.ee.ic.ac.uk/~mrt102/projects/mls.... As I understand, to get an impulse response of a system I need to calculate cross-calculation  of input signal - MLS and output signal of a system.
I tried to do measurements on simple lowpass RC-filter. The result I get is strange, it is a noisy signal that does not look like lowpass filter signal response. I tried to use convolution and circular correlation but it didn't help.
I suspect the problem is related with calculation methods. I calculate correlation using the convolution theorem that allows to calculate convolution using Fourier transforms of signals. But, the article describes Walsh-Hadamard transform to use in the method.
Also I checked the form of MLS, the generated signal is correct, but I am not sure should it be periodic or not.
My questions are:
Can I get wrong results because I don't use Walsh-Hadamard transform during calculations?
Could you, please, give a sample of code in Matlab or Python that calculate correlation using Walsh-Hadamard transform?
Can there be other sources of problems, for example, distortion related with periodicity of MLS-signal?
Thank you in advance.
P.S. I can show screnshots of wrong impulse responses I got if it is required.
The link provided as a reference is broken. But, regardless of what the OP's source says, the Walsh-Hadamard transform method (multiply the data vector with a $2^n\times 2^n$ Hadamard matrix $H_n$ in Sylvester form $$ H_n = \left[\begin{matrix} H_{n-1} &amp; H_{n-1}\\ H_{n-1} &amp; -H_{n-1}\end{matrix}\right]$$ does not give the cross-correlation of the data vector with a binary maximum-length linear feedback shift register sequence (presumably the MLS referred to by the OP) of period $2^n-1$. It is possible to permute the data vector  entries to get a close approximation of the result, indeed even the exact result, of the desired cross-correlation, but just applying the Walsh-Hadamard transform to the unpermuted data vector results in garbage, as the OP has discovered.
A description of how the MLS method works can be found in this answer of mine. The necessary permutations to make the Walsh-Hadamard transform method work are probably there somewhere on this forum.