Analytical Approach for Numerical Accuracy Estimation of Fixed-Point Systems Based on Smooth Operations

In embedded systems using fixed-point arithmetic, converting applications into fixed-point representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixed-point system, which is accurate...

Full description

Saved in:
Bibliographic Details
Published in:IEEE transactions on circuits and systems. I, Regular papers Vol. 59; no. 10; pp. 2326 - 2339
Main Authors: Rocher, R., Menard, D., Scalart, P., Sentieys, O.
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2012
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Accuracy
Accuracy evaluation
adaptive filters
Algorithms
Embedded systems
Fixed points (mathematics)
fixed-point arithmetic
Impulse response
Least mean squares algorithm
Mathematical analysis
Mathematical model
Mathematical models
Matrices
Noise
Numerical models
Object oriented modeling
Quantization
quantization noises
Recursive
Studies
Vectors
ISSN:1549-8328, 1558-0806
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In embedded systems using fixed-point arithmetic, converting applications into fixed-point representations requires a fast and efficient accuracy evaluation. This paper presents a new analytical approach to determine an estimation of the numerical accuracy of a fixed-point system, which is accurate and valid for all systems formulated with smooth operations (e.g., additions, subtractions, multiplications and divisions). The mathematical expression of the system output noise power is determined using matrices to obtain more compact expressions. The proposed approach is based on the determination of the time-varying impulse-response of the system. To speedup computation of the expressions, the impulse response is modelled using a linear prediction approach. The approach is illustrated in the general case of time-varying recursive systems by the Least Mean Square (LMS) algorithm example. Experiments on various and representative applications show the fixed-point accuracy estimation quality of the proposed approach. Moreover, the approach using the linear-prediction approximation is very fast even for recursive systems. A significant speed-up compared to the best known accuracy evaluation approaches is measured even for the most complex benchmarks.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:1549-8328
1558-0806
DOI:10.1109/TCSI.2012.2188938