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Eigenstructure approach for characterization of FIR PR filterbanks with order one polyphase

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2 Author(s)
Murhuvel, A. ; Dept. of Electr. Commun. Eng., Indian Inst. of Sci., Bangalore, India ; Makur, A.

A new approach for the characterization of M-channel finite impulse response (FIR) perfect reconstruction (PR) filterbanks is proposed. By appropriately restricting the eigenstructure of the polyphase matrix of the bank, a complete characterization of order-one polyphase matrices is obtained in which the polynomial part is in a block diagonal form. Nilpotent matrices play a crucial role in the structure. This structure allows imposing restrictions on the order of the inverse of the polyphase matrix and/or analysis-synthesis delay (reconstruction delay). Next, we derive an alternate complete characterization in terms of the degree of the determinant and the McMillan degree of order-one polyphase matrix, which we call the dyadic-based characterization. The characterization of Vaidyanathan and Chen (1995) for matrices with anticausal inverse turns out to be a special case of the proposed characterization. The dyadic-based characterization is more suitable for design without any above-mentioned restriction since it allows better initialization. We finally present design examples with different cost functions

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Signal Processing, IEEE Transactions on  (Volume:49 ,  Issue: 10 )