Filter-generating systems

Combining the methods of generating functions and discrete-time linear systems, we can develop multidimensional (M-D) digital systems for systematic generation of entire families of interrelated digital filters. These M-D systems, dubbed filter-generating systems, are mostly of infinite-impulse response (IIR) type and can produce the impulse response sequence of any member of the family. Temporal and spatio-temporal implementation of filter-generating systems are studied. A temporal implementation scheme is devised for causal filter-generating systems in order to implement an arbitrary filter member using (M-D) signal processing techniques. It is shown that this may result in low order recursive filtering structures that can implement arbitrarily high order members of the family. A spatio-temporal implementation scheme is developed for generation of regular signal flow-graphs for the generated family of finite-impulse response (FIR) filters. It is shown that the signal flow-graphs give rise to cellular array structures. Concrete examples are provided for maximally flat FIR filters.