Filter-generating systems

Combining the methods of generating functions and discrete-time linear syst ems, we can develop multidimensional (M-D) digital systems for systematic g eneration of entire families of interrelated digital filters, These M-D sys tems, dubbed filter-generating systems, are mostly of infinite-impulse resp onse (IIR) type and can produce the impulse response sequence of any member of the family, Temporal and spatio-temporal implementation of filter-gener ating 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 arbit rarily high order members of the family. A spatio-temporal implementation s cheme is developed for generation of regular signal flow-graphs for the gen erated family of finite-impulse response (FIR) filters. It is shown that th e signal flow-graphs give rise to cellular array structures. Concrete examp les are provided for maximally fiat FIR filters.