A Finite Precision Block Floating Point Treatment to Direct Form, Cascaded and Parallel FIR Digital Filters

This paper proposes an efficient finite precision block floating FIR filters when realized in finite precision arithmetic with point (BFP) treatment to the fixed coefficient finite impulse response (FIR) two widely known data formats, namely, fixed-point (FxP) digital filter. The treatment includes effective implementation of all the three and floating-point (FP) representation systems, by investigatforms of the conventional FIR filters, namely, direct form, cascaded and paring the associated quantization errors [1], [6]-[8], [13], [18], allel, and a roundoff error analysis of them in the BFP format. An effective [23], [28], [37]. In all these finite precision studies about block formatting algorithm together with an adaptive scaling factor is proFIR filters, however, it is found out that incorporating FxP posed to make the realizations more simple from hardware view point. To format in any implmentational scheme gives the provision to this end, a generic relation between the tap weight vector length and the input take advantages like less computational complexity and power block length is deduced. The implementation scheme also emphasises on a comsumption. However, the main drawback of this arithmetic simple block exponent update technique to prevent overflow even during the is the limited dynamic range. Such a problem can be eluded block to block transition phase. The roundoff noise is also investigated along using FP format by paying the price of increased hardware the analogous lines, taking into consideration these implementational issues. complexity. In a few other studies, efforts have been made The simulation results show that the BFP roundoff errors depend on the sigto carry out the filter implementation with a viable alternative nal level almost in the same way as floating point roundoff noise, resulting in approximately constant signal to noise ratio over a relatively large dynamic of normalized FP concept, called, block-floating-point (BFP) range. representation [41], [38] where the incoming data is partitioned into non-overlapping blocks and depending on the relaKeywords— Finite impulse response digital filters, Cascade structure, tive magnitudes of the data samples in each block, a common Parallel structure, Block floating point arithmetic, Roundoff error. exponent is assigned. Thus the usual filtering computations under this arithemtic can be carried out in a FxP like man