A minimum-order structure for fixed-point digital filters

The approximation and optimal implementation of a digital filter with fixed-point arithmetic are investigated. A minimum-order structure is derived which minimizes an upper bound error due to the order approximation and output round-off noise. It is found that the minimum-order structure exhibits some favorable properties, such as absence of limit cycle and robustness of the filter´s constant coefficients. A numerical example is presented to illustrate the proposed design technique