Derivation and stability analysis of multidimensional IIR block digital filters

This paper describes two methods of constructing multidimensional block systems and polyphase networks from a given scalar system. The stability of the block system is also investigated. It is shown that the poles of the block system are closer to the origin than the poles of its scalar counterpart. Moreover, the scalar transfer function can be derived from the block transfer function. Finally, we show that the scalar and block systems have the same overall input-output map although the properties and architectures of the systems are quite different.