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Design of complex-coefficient variable digital filters using successive vector-array decomposition

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1 Author(s)
Tian-Bo Deng ; Dept. of Inf. Sci., Toho Univ., Chiba, Japan

Singular-value decomposition (SVD) can be efficiently utilized to obtain the optimal vector-array decomposition (VAD) for simplifying real-coefficient variable digital filter design problem, but the SVD-based VAD methods are not applicable to the design of complex-coefficient variable filters. This paper proposes a successive algorithm for decomposing arbitrary multidimensional complex array into the VAD form, and thus, a complex-coefficient variable digital filter with arbitrary variable frequency response can be easily obtained through constant complex-coefficient filter design and multidimensional polynomial fitting. The new VAD algorithm successively decomposes the complex array and its residual arrays into the vector-array pairs stage by stage, and each stage contains an iterative optimization that can be easily solved in a closed-form. Our computer simulations have demonstrated that the successive VAD converges very fast to the optimal solution.

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Circuits and Systems I: Regular Papers, IEEE Transactions on  (Volume:52 ,  Issue: 5 )