Round-Off Noise of Multiplicative FIR Filters Implemented on an FPGA Platform

Jean-Jacques Vandenbussche,Peter Lee,Joan Peuteman

doi:10.3390/app4020099

Jean-Jacques Vandenbussche, Peter Lee + Show 1 more

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https://doi.org/10.3390/app4020099

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Journal: Applied sciences	Publication Date: Mar 25, 2014
Citations: 18	License type: CC BY 4.0

Affiliation: KU Leuven, University of Kent

Abstract

The paper analyzes the effects of round-off noise on Multiplicative Finite Impulse Response (MFIR) filters used to approximate the behavior of pole filters. General expressions to calculate the signal to round-off noise ratio of a cascade structure of Finite Impulse Response (FIR) filters are obtained and applied on the special case of MFIR filters. The analysis is based on fixed-point implementations, which are most common in digital signal processing algorithms implemented in Field-Programmable Gate-Array (FPGA) technology. Three well known scaling methods, i.e., L2 bound; infinity bound and absolute bound scaling are considered and compared. The paper shows that the ordering of the MFIR stages, in combination with the scaling methods, have an important impact on the round-off noise. An optimal ordering of the stages for a chosen scaling method can improve the round-off noise performance by 20 dB.

Highlights

Multiplicative Finite Impulse Response (MFIR) filters are a class of filter structures that were originally introduced by Fam in the early 1980s [1]
As in this correspondence the implementation of the MFIR filters is investigated for fixed-point implementation, the rounding process is of vital importance
An approach to model round-off noise in general cascade filter structures has been studied. This round-off noise depends on the used scaling method and on the ordering of the stages

Summary

Introduction

Multiplicative Finite Impulse Response (MFIR) filters are a class of filter structures that were originally introduced by Fam in the early 1980s [1]. A. Fam developed, in [1], the “pure multiplicity property” which forms the basis of the investigation of the relationship between the noise variance at the output (relative to the round-off noise variance) and the ordering of the different stages of the MFIR filter. In [1], the “pure multiplicity property” which forms the basis of the investigation of the relationship between the noise variance at the output (relative to the round-off noise variance) and the ordering of the different stages of the MFIR filter This is done for an implementation without scaling (which is not very realistic for fixed point implementations) and an implementation with L2 scaling. The approximation of a conjugate pole pair in cascade is not analyzed as “it does not have the pure multiplicity property” [1]

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