Digital signal-processing structure and methodology which feature a time-slice-based digital fabricating engine, and software operating structure operatively associated with that engine structured to operate the engine in a time-slice-based fabrication mode wherein the engine, in a time-differentiated and instantiating manner, functions to fabricate a time-succession of individual, composite wave digital filters. Each of these filters takes the form of (1) a concatenated assembly including one to a plurality of upstream, early-stage, decimate-by-two, signal-processing agencies connected in a cascade series arrangement, with each such agency possessing a first transfer function having a first transition bandwidth, and (2) a single, downstream, later-stage, decimate-by-two, signal-processing agency which possesses a second transfer function having a transition bandwidth which is less than the mentioned first transition bandwidth.