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

**Authors:**
Abhijit Mitra

**Abstract:**

This paper proposes an efficient finite precision block floating point (BFP) treatment to the fixed coefficient finite impulse response (FIR) digital filter. The treatment includes effective implementation of all the three forms of the conventional FIR filters, namely, direct form, cascaded and par- allel, and a roundoff error analysis of them in the BFP format. An effective block formatting algorithm together with an adaptive scaling factor is pro- posed to make the realizations more simple from hardware view point. To this end, a generic relation between the tap weight vector length and the input block length is deduced. The implementation scheme also emphasises on a simple block exponent update technique to prevent overflow even during the block to block transition phase. The roundoff noise is also investigated along the analogous lines, taking into consideration these implementational issues. The simulation results show that the BFP roundoff errors depend on the sig- 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 range.

**Keywords:**
Finite impulse response digital filters,
Cascade structure,
Parallel
structure,
Block floating point arithmetic,
Roundoff error.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1079266

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