Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2N additions, 2 (N + 1) memory units, and N + 1 multipliers for the N + 1 -point Hermite and binomial transforms. The recursive flow diagram for the N + I-point Laguerre transform requires 2N additions, 2(N + 1) memory units, and 2(N + 1) multipliers. The transform computation time for all of these transforms is O(N).