Reduced multiplier, low roundoff noise digital filters

Minimal roundoff noise IIR digital filters require (n+1)²multiplies per output sample for an nth order filter. By optimizing second-order sections which are then parelleled or cascaded, one can reduce this to approximately 4n multiplies per output. This compares to approximately 3n multiplies for the direct form. This paper presents explicit design equation and noise performance equations for low roundoff noise, second-order filters with fewer multipliers than optimal forms. These structures are a compromise between direct forms (minimal number of multipliers) and minimal roundoff noise structures.