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

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Kanat Suleimenov
Kanat Suleimenov 2020-12-27
评论： Ameer Hamza 2020-12-31
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!

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Ameer Hamza
Ameer Hamza 2020-12-27
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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