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How do I compute a level-four Hankel matrix ?

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Yapo OBOUE
Yapo OBOUE on 22 Jun 2019
Hello everyone, I am trying to embed a 4-D spatial hypercube Dk1, k2, k3, k4 in a level-four block Hankel matrix as follows. I need to first embed the data in a level-one Hankel matrix using all data components in the first dimension of the tensor Dk1,k2,k3,k4 at a given frequency w0. I have to addressed in advance that each frequency slice of data is operated the exactly same way. I need to operate in the following way :
  • first, embed the data in a level-one Hankel matrix using all data components in the first dimension of the tensor Dk1,k2,k3,k4 at a given frequency w0.
  • then, these matrices are embedded gradually in a level-two, three and level-four block Hankel matrices.
The level-four is the target matrix of my problem. The size of level-four block Hankel matrix M(4) is (Y1Y2Y3Y4) × (X1Y1 + 1)(X2Y2+ 1)(X3Y3 + 1)(X4Y4 + 1). If Xi is an odd integer, the size of M(4) is (Y1Y2Y3Y4) × (Y1Y2Y3Y4).
You will find attached more detail about my concern.
I trying to compute these matrices in oder to get target matrix (level-four) but I meet a lot difficulties. I need any help that could help me to get my target.
Thanks for giving me a hand.

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