Roundoff Noise Minimization in Digital Filters with Application to Two-Dimensional Filters
L.M. Smith, Bruce W. Bomar · 1988
Abarwt-A new rJeoritlun is presented for mininizing rounddl noise effects in stntc-sp.oe implementations of recursive digital filters while cMq certain caefficients to be zero. Beginning witb a direct form strurture, the algorithm mses the scaling (K) and Mire ( W) mnbices to iteratively eonsbuct U( upper oc lower triangular trPnsfonnation trh to apply to the original state-space model. The result is a structure dtb I savings of fN(N - 1) multiplies over th minimum noise struuure. l%e technique is of mt utility in the realization of two-dimensional filters that cannot, in general, be factored into the Ppnw or cascade MrmerfloR of lower order subfilters Because of the sparse ~hw of the bed statespace stnrehlrc eoeffiiient matrices in two-dimensional direct- and contrdler-fonn rorliutbns, trnndonaing with an upper and lower triangular Madr diqpnd trpmfonnatian matrix retains many zeroes in the shucturp md results in 8 low rounddf noise, computationally effiint state-spnx realization. A nm controller fom state-space smcture for a general two-dimensional transfer function is presented to whidt the noise minimization procedure is didy applicable. Numerical examples are presented to &bate the applicability of this algorithm to both oneand tno-dlnensiod filters. In dl cases, the noise gain of fie= realized wlth this technique Is extremely dose to the minimum achkpM0.