Block-state recursive digital filters with minimum round-off noise

The development of a block state-structure with minimum round-off noise subject to ℓ2-norm dynamic range constraint is outlined. The pertinent equations for scaling and for round-off noise analysis of block-state structures are first derived. Next, a lower bound and the global minimum of the output noise due to the round-off of the block-state variables are derived. A method of deriving the minimum round-off noise block state-structure is outlined. A numerical example is included. With regard to computational complexity and overall noise performance, the block state realization of recursive digital filters is shown to be superior.