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On the design of multiband transmission functions synthesized by one wave digital lattice structure
Author(s) -
Yaseen M.
Publication year - 2013
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.826
Subject(s) - lattice (music) , mathematics , polynomial , degree (music) , function (biology) , digital filter , wavenumber , interpolation (computer graphics) , discrete mathematics , combinatorics , mathematical analysis , filter (signal processing) , physics , computer science , quantum mechanics , telecommunications , frame (networking) , evolutionary biology , acoustics , computer vision , biology
SUMMARY In this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n , which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti‐Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q , the two subpolynomials are calculated and the two branch all‐pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example. Copyright © 2011 John Wiley & Sons, Ltd.