Signal and system representations on hyperbolic groups: Beyond rational orthogonal bases

This paper investigates signal and system representations in special rational orthogonal bases of the Hardy space H². These bases are derived from the Blaschke-group associated to the hyperbolic group SH(n) of matrices. Using the concept of the unitary group representations over H², and the voice-transform, specific hyperbolic wavelet constructions - Blaschke-wavelets and the associated Blaschke-Fourier transform are constructed. State space representations of systems over hyperbolic groups are discussed, too, with the purpose to explore the perspectives of elaborating a unified system theory upon this conceptual base.