An optimization procedure to minimize the roundoff noise in cascade floating-point digital filters

The authors study the roundoff errors in floating-point arithmetic and present an optimization procedure for cascade floating-point digital filters. Applying the isosceles trapezoidal distribution to the error analysis of cascade floating-point digital filters, they have obtained results that are in extremely close agreement with computer simulation values. Using the optimization procedure, a near-optimal pole ordering that minimizes the output roundoff noise is quickly found. Examples that demonstrate the importance of applying an optimization procedure even to floating-point digital filters are presented. The procedure is extremely effective for reducing the roundoff noise of high-order cascade floating-point digital filters