Computationally efficient second-order digital filter sections with low roundoff noise gain

A class of second-order recursive digital filter realizations is described that provides near-optimal roundoff noise performance, low-coefficient sensitivity, and freedom from overflow limit cycles. The number of multiplications required, per output sample, is one more than the canonical direct form realization. This class of realizations provides an attractive compromise between the computationally intensive optimal realization and the finite-word-sensitive direct form. Explicit design procedures are provided, and a numerical design example is presented that illustrates the near-optimal performance of this new class of realizations.