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

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!

Answer 1

[Ameer Hamza]

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, [])

[Kanat Suleimenov]

Dear Ameer, thank you for your answer, It gives me the same solution as I want, but what is the k in this code? In my case k is the time instant.

[Ameer Hamza]

In my code, k is number of rows in this form of matrix Y: Y = [y(1) y(2) y(3) y(4); y(2) y(3) y(4) y(5)]. Use some other name instead of 'k' if it conflict it with a variable in your code.

[Kanat Suleimenov]

Dear Ameer, thanks for your help. It works now. Wish you best!

[Ameer Hamza]

I am glad to be of help!