Structures for generating polynomial responses

Two computationally efficient recursive structures are introduced for generating arbitrary polynomial responses. For an Mth-order polynomial, M+1 coefficients are required to obtain the desired shape regardless of the length of the response. For truncating the response, M+1 additional integer-valued coefficients are needed. The proposed structures can be used in a straightforward manner for constructing computationally efficient predictors as well as linear-phase FIR filters with piecewise-polynomial impulse responses