Minimum roundoff noise digital filters with some power-of-two coefficients

A new technique and numerical algorithm are introduced for synthesizingnth-order minimum roundoff noise state-space structures for nth-order fixed-point recursive digital filters. The technique yields structures which employ(n² - n -1)trivial power-of-two multiplies and so require only(3n + 2)nontrivial multiplies. This compares to the(n + 1)²nontrivial multiplies required by other minimum-noise structures. Although the power-of-two structures do not satisfy theoretical conditions for roundoff noise optimality, their roundoff noise is found to be but negligibly higher than minimum. A numerical example illustrating the synthesis technique is provided.