Realization of Digital Filters Using Block- Floating-point
A.V. Oppenheim · 1970
Recently, statistical models for the effects of roundoff noise in fixed- point and floating-point realizations of digital filters have been pro- posed and verified, and a comparison between these realizations pre- sented. In this paper a structure for implementing digital filters using block-floating-point arithmetic is proposed and a statistical analysis of the effects of roundoff noise is carried out. On the basis of this analysis, block-floating-point is compared to fixed-point and floating- point arithmetic with regard to roundoff noise effects. A Structure for Block-Floating-point Realization In block-floating-point arithmetic the input and filter states (Le., the outputs of the delay registers) are jointly normalized before the multiplications and adds are per- formed using fixed-point arithmetic. The scale factor obtained during the normalization is then applied to the final output to produce a fixed-point result. To illustrate, consider a first-order filter described by the difference equation