Discrete polynomial transform representation using binary matrices and flow diagrams

This paper presents a new method for computing discrete polynomial transforms. The method is shown for the Hermite, binomial, and Laguerre transforms. The new method factors Pascal's matrix into binary matrices. Constructing the flow diagrams for the transform matrices requires only additions and N-2 multipliers for N-point Hermite and binomial transforms, and 2N multipliers for an N-point Laguerre transform. The method involves a three-stage process where stages 1 and 3 are identical for all three transforms.