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Title: Construction of conjugate quadrature filters with specified zeros
Authors: Lawton, W. 
Micchelli, C.A.
Keywords: Conjugate quadrature filter
Laurent polynomials
Polynomial approximation
Spectral factorization
Issue Date: 1997
Citation: Lawton, W.,Micchelli, C.A. (1997). Construction of conjugate quadrature filters with specified zeros. Numerical Algorithms 14 (4) : 383-399. ScholarBank@NUS Repository.
Abstract: Let ℂ denote the complex numbers and ℒ denote the ring of complex-valued Laurent polynomial functions on ℂ \ {0}. Furthermore, we denote by ℒR, ℒN the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that for any two Laurent polynomials P1, P2 ∈ ℒN, which have no common zeros in ℂ \ {0} there exists a pair of Laurent polynomials Q1, Q2 ∈ ℒN satisfying the equation Q1P1 + Q2P2 = 1. We provide some information about the minimal length Laurent polynomials Q1 and Q2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter whose zeros contain an arbitrary finite subset Λ ⊂ ℂ \ {0} with the property that for every λ, μ ∈ Λ, λ ≠ μ implies λ ≠ -μ and λ ≠ -1/μ̄.
Source Title: Numerical Algorithms
ISSN: 10171398
Appears in Collections:Staff Publications

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