Editing Digital filter (section)

===Direct form II===

The alternate [[Digital biquad filter#Direct form 2|direct form II]] only needs ''N'' delay units, where ''N'' is the order of the filter – potentially half as much as direct form I.  This structure is obtained by reversing the order of the numerator and denominator sections of Direct Form I, since they are in fact two linear systems, and the commutativity property applies. Then, one will notice that there are two columns of delays (<math>z^{-1}</math>) that tap off the center net, and these can be combined since they are redundant, yielding the implementation as shown below.

The disadvantage is that direct form II increases the possibility of arithmetic overflow for filters of high ''Q'' or resonance.<ref>J. O. Smith III, [http://ccrma.stanford.edu/~jos/filters/Direct_Form_II.html Direct Form II]</ref>  It has been shown that as ''Q'' increases,  the round-off noise of both direct form topologies increases without bounds.<ref>L. B. Jackson, "On the Interaction of Roundoff Noise and Dynamic Range in Digital Filters," ''Bell Sys. Tech. J.'', vol. 49 (1970 Feb.), reprinted in ''Digital Signal Process'', L. R. Rabiner and C. M. Rader, Eds. (IEEE Press, New York, 1972).</ref>  This is because, conceptually, the signal is first passed through an all-pole filter (which normally boosts gain at the resonant frequencies) before the result of that is saturated, then passed through an all-zero filter (which often attenuates much of what the all-pole half amplifies).

[[File:Biquad filter DF-II.svg|400px]]