We show that the uncertainty determined by the minimum division of a measuring instrument can be diminished by using dithering. We present a numerical example to introduce the technique and two experiments that show how the precision is enhanced.
REFERENCES
1.
D. C. Baird, Experimentation (Prentice–Hall, Englewood Cliffs, 1988), Secs. 2–3.
2.
P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1992), Secs. 2–4.
3.
K. Sommer and M. Kochsiek, “Role of measurement in deciding conformance in legal metrology,” OIML-Bulletin XLIII, 2002, pp. 19–24.
4.
L.
Schuchman
, “Dither signals and their effect on quantization noise
,” IEEE Trans. Commun. Technol.
COM-12
, 162
–165
(1964
).5.
D.
Tweed
, “Digital processing in an analog world: Dithering your conversion
,” Circuit Cellar INK
101
, 68
–72
(1998
), or 〈http://www.dtweed.com〉.6.
A. V. Oppenheim and R. W. Schaffer, Digital Signal Processing (Prentice–Hall, Englewood Cliffs, 1975).
7.
W. R.
Bennet
, “Spectra of quantized signals
,” Bell Syst. Tech. J.
27
, 446
–472
(1948
).8.
B.
Widrow
, “Statistical analysis of amplitude quantized sampled-data systems
,” Trans. Am. Inst. Electr. Eng.
79
, 555
–568
(1960
).9.
L. G.
Roberts
, “Picture coding using pseudo-random noise
,” IRE Trans. Inf. Theory
8
, 145
–154
(1962
).10.
L.
Gammaitoni
, “Stochastic resonance and the dithering effect in threshold physical systems
,” Phys. Rev. E
52
, 4691
–4698
(1995
).11.
R. A.
Wannamaker
, S. P.
Lipshitz
, and J.
Vanderkooy
, “Stochastic resonance as dithering
,” Phys. Rev. E
61
, 233
–236
(2000
).12.
N. G.
Stocks
, “Suprathreshold stochastic resonance in multilevel threshold systems
,” Phys. Rev. Lett.
84
, 2310
–2313
(2000
).13.
E. B. Loewenstein, “Reducing the effects of noise in a data acquisition system by averaging,” AN152, National Instruments “6023E/6024E/6025E User’s Manual,” National Instruments, 2000, 〈http://www.ni.com〉;
“Enhanced resolution in LeCroy digital oscilloscopes,” Application Notes, LeCroy, 〈http://www.lecroy.com〉;
“TDS500 Series Digital Phosphor Oscilloscopes,” User’s Manual, Tektronix, 〈http://www.tektronix.com〉.
14.
MultiPurpose Lab Interface, Teacher’s Guide, Vernier Software, 1994, p. 28.
15.
J. M.
Simon
, M. C.
Simon
, and C. E.
Vanney
, “Systematic errors, statistical errors: A demonstrative experience
,” Anales AFA
5
, 1
–4
(1993
).16.
Reference 2, Sec. 4, p. 57.
This content is only available via PDF.
© 2004 American Association of Physics Teachers.
2004
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.
