A flexible engine for implementing digital signal processing (DSP) functions involving repeating various arithmetic/logical operations on a stream of data includes multiple programmable filter elements, at least one of which includes a microcode control program for internal control of the programmable filter element. The engine also includes programmable interconnection logic coupled to the programmable filter elements for selectively combining, scaling, and accumulating output values from the first plurality of programmable filter elements and selectively providing accumulated values as inputs to the first plurality of programmable filter elements. A filter controller coupled to the programmable filter elements and the programmable interconnection logic includes its own microcode control program for external control of the programmable filter elements and the programmable interconnection logic. Multiple engines can be combined to form larger, more powerful engines.