Abstract
The accuracy of data recorded by many measurement systems is limited both by uncertainty in the measured value as well as by uncertainty in the trigger input to the system which controls when a measurement is taken. The former effect, which appears as noise on the underlying signal, is due, in part, to the sampling process and can often be reduced to an acceptable level by averaging many measurements. Noise on the trigger input gives rise to uncertainty in time between the trigger and the measurement points. The effect, known as jitter, causes a distortion of the signal which cannot be removed by averaging.
We describe and analyse the effects of noise and jitter on a waveform, and an algorithm for removing, or reducing, these effects is presented. The work is motivated by an application in picosecond electrical and optoelectronic metrology where a laser pulse is measured by a system consisting of a photodiode and sampling oscilloscope. Here, since the length of the pulse is so short, perhaps only tens of picoseconds in duration, the effect of jitter is as pronounced as that of measurement noise. Results obtained by applying the algorithm to simulated data obtained from this application are presented.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G.T. Anthony and M.G. Cox, The National Physical Laboratory's Data Approximation Subroutine Library, in:Algorithms for Approximation, eds. J.C. Mason and M.G. Cox (Clarendon Press, Oxford, 1987) pp. 669–687. Also National Physical Laboratory DITC Report No. 71/86.
M.G. Cox, P.M. Harris and H.M. Jones, Strategies for knot placement in least squares data fitting by splines, NPL Report DITC 101/87 (1987).
M.G. Cox, P.M. Harris and H.M. Jones, A knot-placement strategy for least-squares spline fitting based on the use of local polynomial approximations, in:Algorithms for Approximation II, eds. J.C. Mason and M.G. Cox (Chapman and Hall, London, 1988) pp. 37–45. Also National Physical Laboratory DITC Report No. 148/89.
M.G. Cox, The numerical evaluation of B-splines, J. Inst. Math. Appl. 10 (1972) 134–149.
M.G. Cox, Practical spline approximation, in:Lecture Notes in Mathematics 965: Topics in Numerical Analysis, ed. P.R. Turner (Springer, Berlin, 1982) pp. 79–112. Also National Physical Laboratory DITC Report No. 1/82.
C. de Boor, On calculating with B-splines, J. Approx. Theory 6 (1972) 50–62.
C. de Boor,A Practical Guide to Splines (Springer, New York, 1978).
B. Efron,The Jackknife, the Bootstrap and Other Resampling Plans (Society for Industrial and Applied Mathematics, Philadelphia, 1982).
D.A. Humphreys, Measurement techniques, numerical methods and photodiode risetime transfer standards for picosecond optoelectronic device metrology at 1–1.6Μm, PhD thesis, University of London (1990).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cox, M.G., Harris, P.M. & Humphreys, D.A. An algorithm for the removal of noise and jitter in signals and its application to picosecond electrical measurement. Numer Algor 5, 491–508 (1993). https://doi.org/10.1007/BF02108665
Issue Date:
DOI: https://doi.org/10.1007/BF02108665