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.