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.