Derivation of an expression for the roundoff noise determinant det (KW)^{1/2} for digital filters

The minimal roundoff noise in fixed point digital filters is determined by a certain determinant, generally denoted by det(KW)^{1/2}. This determinant may be expressed by the poles and zeros of the filter transfer function H(z). This paper presents a simple and direct derivation of this expression, based upon an expansion of H(z) in partial fractions of the first order.