Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm

@article{Hndel2000PropertiesOT,
  title={Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm},
  author={P. H{\"a}ndel},
  journal={IEEE Trans. Instrum. Meas.},
  year={2000},
  volume={49},
  pages={1189-1193}
}
  • P. Händel
  • Published 2000
  • Mathematics, Computer Science
  • IEEE Trans. Instrum. Meas.
The IEEE Standard 1057 (IEEE-STD-1057) provides algorithms for fitting the parameters of a sine wave to noisy discrete time observations. The fit is obtained as an approximate minimizer of the sum of squared errors, i.e., the difference between observations and model output. The contributions of this paper include a comparison of the performance of the four-parameter algorithm in the standard with the Cramer-Rao lower bound on accuracy, and with the performance of a nonlinear least squares… Expand
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References

SHOWING 1-10 OF 13 REFERENCES
Comparative evaluation of computer methods for calculating the best-fit sinusoid to the digital record of a high-purity sine wave
TLDR
A comparative evaluation of programs used in the “equivalent bit” test is described, both in terms of how often each method converged and also of how much computer time each method took to converge. Expand
A comparative evaluation of some practical algorithms used in the equivalent bits test of waveform recorders
A comparative evaluation of three basic algorithms that are used in the equivalent-bit test in digital recorders is presented. The algorithms are used to calculate the parameters of a pure sinusoidExpand
Overview of IEEE-STD-1241 "standard for terminology and test methods for analog-to-digital converters"
IEEE-STD-1241 has been drafted and is being revised this year to prepare for ballot and publishing. A year ago, the IEEE office asked us to also coordinate its release with the IEC to make it a fullExpand
Waveform recorder testing: IEEE standard 1057 and You
  • T. Linnenbrink
  • Engineering
  • Proceedings of 1995 IEEE Instrumentation and Measurement Technology Conference - IMTC '95
  • 1995
Waveform recorders and digital oscilloscopes have become indispensable tools for electronics measurement and diagnosis. However, because they are complex, sophisticated instruments, it is oftenExpand
Fundamentals of statistical signal processing: estimation theory
Minimum variance unbiased estimation Cramer-Rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squaresExpand
IEEE Standard for digitizing waveform recorders
  • IEEE Standard
  • 1057
Introduction to Spectral Analysis, Prentice-Hall
  • Upper Saddle River, NJ,
  • 1997
A comparative evaluation of some practical algorithms used in the effective bits test of waveform recorders
  • IEEE Transactions on Instrumentation and Measurement,
  • 1989
System identification
Comparative evaluation of computer methods for calculating the best fit sinusoid to the high purity sine wave
  • IEEE Transactions on Instrumentation and Measurement, Vol. IM-36,
  • 1987
...
1
2
...