Optimal roundoff noise selection in class of minimal canonical nonproduct of multiplier digital filters

A study is presented for the roundoff performance of a class of
m
th-order digital filters known as minimal canonical nonproduct of multiplier in which a minimum amount of delay units
( \leq m)
, multipliers
( \leq 2 m)
, and 2-input adders
(\leq 2 m)
are used with the constraint that their transfer function expressions do not contain product of multiplier coefficient terms. An expression for roundoff noise gain is developed. This expression is useful in selecting structures with minimum roundoff noise among all existing equivalent structures of the previously mentioned class of digital filters.