Multiplier-free structures for exact generation of natural powers of integers

It is shown that the sequence of an arbitrary natural power of consecutive integers can be generated without any multiplications as the impulse response of a multirate recursive structure. This multistage structure has a regular configuration consisting of multirate building blocks and accumulators. A nonrecursive structure is also developed for the generation of the power sequence for a prescribed finite length. This feedforward structure consists of layers of summation nodes interconnected in a regular manner. The two types of multiplier-free discrete-time structures generate the exact values of natural kth powers of consecutive integers in a simple, regular and scalable manner.