Optimization of digital filters for low roundoff noise

This paper treats the problem of minimizing the roundoff noise in digital filters using fixed-point arithmetic under sinusoidal input. A basic assumption made is that of representing the roundoff error as white noise that is independent from sample to sample and from source to source. The minimax noise principle is introduced to serve as a guide in the filter design to optimize the structure for minimum noise. One application is illustrated through the design of low-noise cascade digital filters under dynamic range constraints. Numerical examples demonstrate the lower noise possible in comparison to other known designs and serve to verify the effectiveness of a design procedure based on the minimax concept.