Synthesis of minimum roundoff noise fixed point digital filters

Roundoff noise and scaling in the digital implementation of control compensators

“…The (unscaled) state covariance matrix Z for (9) can be written (as in [19][20][21]) assuming a unit-variance Gaussian noise input y(k), as the solution of a steady-state Lyapunov equation:…”

“…As stated in the introduction, we will adapt a method used in evaluating digital filter roundoff effects [18][19][20][21]. As in most digital filtering applications, we will assume a uniform wordlength of the internal registers of the compensator.…”

“…In most filtering applications, the filter output variance due to roundoff quantization is taken to be the measure of performance for the structure [3, [18][19][20][21]25]. The analysis of roundoff effects is based on the following assumption.…”

“…Mullis and Roberts [19,20] and Hwang [211 have developed techniques for computing structures with minimum roundoff noise effects.…”

“…Roberts [19,20] and Hwang [21] will be adapted for controllers in Section 6, along with a treatment of the more general optimization techniques introduced by Chan, also as adapted for controller implementation. Finally, (using the techniques we have developed) we will compare the roundoff quantization noise performance of several scaled structures for implementing a specific LQG controller example.…”