Browse Prior Art Database

Noise averaging and measurement resolution

IP.com Disclosure Number: IPCOM000125645D
Original Publication Date: 1999-Apr-01
Included in the Prior Art Database: 2005-Jun-09
Document File: 3 page(s) / 79K

Publishing Venue

National Institute of Standards and Technology

Related People

James Potzick: INVENTOR

Abstract

When making high accuracy dimensional measurements, great pains are often taken to reduce the vibration level in the measurement apparatus because vibration contributes to the variance of the measurement readings. On the other hand, it is common practice in the audio recording industry to add dither, in the form of noise, to an audio signal prior to analog-to-digital (A/D) conversion to reduce the audible effects of quantization. This suggests that, when A/D resolution is a significant component of measurement uncertainty and the sample rate is high enough to allow over sampling and averaging, heroic attempts at noise reduction may be counterproductive.

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REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 70, NUMBER 4 APRIL 1999

...

Noise averaging and measurement resolution

"or ''A little noise

is a good thing''

James Potzicka)

National Institute of Standards and Technology, Gaithersburg, Maryland 20899 [H20849]Received 6 October 1998; accepted for publication 15 January 1999[H20850]

When a continuous quantity is measured with a digital instrument or digitized for further processing, a measurement uncertainty component is incurred from quantization of the continuous variable. This uncertainty can be reduced by oversampling and averaging multiple measurements, but only if there is some noise on the measurand. In this article the optimum noise level is determined, and the subsequent improvement in measurement uncertainty calculated. [H20851]S0034-6748[H20849]99[H20850]04604-3[H20852]

INTRODUCTION

  When making high accuracy dimensional measurements, great pains are often taken to reduce the vibration level in the measurement apparatus because vibration contributes to the variance of the measurement readings. On the other hand, it is common practice in the audio recording industry to add dither, in the form of noise, to an audio signal prior to analog-to-digital Ã/D[H20850] conversion to reduce the audible ef- fects of quantization. This suggests that, when A/D resolu- tion is a significant component of measurement uncertainty and the sample rate is high enough to allow oversampling and averaging, heroic attempts at noise reduction may be counterproductive.

ANALOG-TO-DIGITAL CONVERSION

  Many measurements involve A/D conversion because the data are often processed in a computer. Voltage A/D converters and displacement measuring interferometers con- vert continuous quantities voltage or position into digital numbers, with a resolution of one least significant bit [H20849]LSB[H20850].

  The most benign model of an A/D converter produces a discrete output y equal to the continuous input x rounded to the nearest LSB. The transfer function y and quantization error [H9280] are

y[H11005]round[H20849]x[H20850], [H9280] [H11005]x[H11002]y.

That is, y[H11005]0 for any [H11002] 12[H11088]x[H11021][H11001] 12 and y[H11005]1 for any 12[H11088]x [H11021]1 12, etc. This transfer function and error function are plot- ted in Fig. 1. This quantization process produces an average error or bias of zero, but adds measurement uncertainty be- cause the actual error is not known.1

MEASUREMENT UNCERTAINTY

  In general, the error [H9280] is the difference between the true value of the measurand and the indicated value.2 In the ab- sence of bias the International Organization for Standardiza-

tion ÎSO[H20850] expanded (k[H11005]2) measurement uncertainty is twice the square root of the variance of the error,3 and can be expressed as

u[H11005]2

[L20881][H20885][H11002][H11009]

[H11009]p[H20849][H9280] [H20850][H9280] 2d[H9280] ,

where p([H9280] ) is the normalized probability density function of the possible values of the error,...