Multiplier-Free Structures for Exact Generation of Natural Powers of Integers
S. Samadi, M. Omair Ahmad, M.N.S. Swamy · 2005
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 k/sup th/ powers of consecutive integers in a simple, regular and scalable manner.