1998 | OriginalPaper | Buchkapitel
Algebra of multirate structures
verfasst von : Richard Tolimieri, Myoung An
Erschienen in: Time-Frequency Representations
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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In this chapter we develop the algebra underlying multirate filter structures over free abelian groups of finite rank. Suppose A is a free abelian group of rank N. Each subgroup Δ of A is a free abelian group of rank n ≤ N. The basis theorem describes how Δ sits in A in the sense that it characterizes the quotient group A/Δ. This quotient group can be a finite abelian groupa free abelian group of finite rankthe direct product of a finite abelian group and a free abelian group of finite rank.