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On necessary and sufficient conditions for perfect reconstruction multidimensional delay chain systems

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3 Author(s)
Xiang-Gen Xia ; Dept. of Electr. & Comput. Eng., Air Force Inst. of Technol., Wright-Patterson AFB, OH, USA ; B. W. Suter ; M. E. Oxley

We present some necessary and sufficient conditions for a perfect reconstruction (PR) modified multidimensional (MD) delay chain system. With these results, one is able to systematically check if a D-dimensional delay chain system with a D×D sampling matrix M and a D×D delay matrix L has a PR property in a simpler way than before, where the matrix module operations are avoided. Moreover, given a D×D sampling matrix M, in many cases one can determine all possible D×D delay matrices L so that the delay chain systems with the sampling matrix M have a PR property. Several examples are provided. We also present a method to generate D×D sampling and delay matrices M and L such that their corresponding traditional MD delay chain systems are PR

Published in:

IEEE Transactions on Signal Processing  (Volume:43 ,  Issue: 6 )