This paper presents a method for analytical and numerical investigatio
n of the reflection and absorption properties of a multilayered quasip
eriodic structure. The structure consists of an arbitrary number of id
entical composite cells. The composite cells contain two magnetodielec
tric layers and a resistive film between them. There are no restrictio
ns on the materials of the layers. The method presented in this paper
is based on a theory of matrix polynomials and resistive boundary cond
itions. The obtained formulas for reflection and transmission coeffici
ents have simple and analyzable form. The method is efficient for a va
riety of multilayered quasiperiodic structures. Under special conditio
ns the considered structure can be used for analysis of its half infin
ite analogue.