Filter Banks on Discrete Abelian Groups

2016/03/10 by Garcia, Antonio Garcia, Hernandez-Medina, Miguel Angel, Perez-Villalon, Gerardo
#FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1603.03330

Abstract

In this work we provide polyphase, modulation, and frame theoretical analyses of a filter bank on a discrete abelian group. Thus, multidimensional or cyclic filter banks as well as filter banks for signals in ℓ²(ℤ^d× ℤ_s) or ℓ²(ℤ_r × ℤ_s) spaces are studied in a unified way. We obtain perfect reconstruction conditions and the corresponding frame bounds.

Related

• Semi-direct product of groups, filter banks and sampling
• Geometric Aspects of Frame Representations of Abelian Groups
• Convolution systems on discrete abelian groups as a unifying strategy in sampling theory
• Riesz and frame systems generated by unitary actions of discrete groups
• Generalized low-pass filters and multiresolution analyses