How can I generate the Hankel matrix using the measured datapoints?

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Dear Researchers, how can I generate a Hankel matrix based on the available data?
For instance, I have the measured data as y = [0 1 3 5 7; 0 2 4 6 8]; I want to generate the Hankel matrix as Y = [y(1) y(2) y(3) y(4); y(2) y(3) y(4) y(5)], where y(k) represents the measured data at k-th time instance, i.e. y(1) = [0; 0], so y(k) is a 2x1 column vector. So, I want to generate the Hankel matrix in which each element is a 2x1 column vector. In my case, I want to get this matrix Y = [0 1 3 5; 0 2 4 6; 1 3 5 7; 2 4 6 8]. This matrix y is taken just for demonstration purpose. It would be better if you suggest solution for high dimension data matrix. This help will be valuable for me! Thanks!

Accepted Answer

Ameer Hamza
Ameer Hamza on 27 Dec 2020
Try something like this
y = [0 1 3 5 7; 0 2 4 6 8];
k = 2; % Y rows in output matrix
[m, n] = size(y);
i = hankel(1:n);
i = i(1:k, 1:end-1);
Y = reshape(y(:,i), m*k, [])
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