IEEE Standard 1057, Cramér-Rao Bound and the Parsimony Principle

This paper deals with some fundamental properties of the sine-wave-fit algorithm included in IEEE Standards 1057 and 1241. Asymptotic Cramer-Rao bounds (CRBs) for three and four model parameters are derived under the Gaussian assump- tion. Further, the sine-wave-fitting properties of the algorithm are analyzed by the parsimony principle. A decision criterion whether to use the three- or four-parameter model is derived. It is shown that a three-parameter sine-wave fit produces a better fit than the four-parameter fit if the frequency is known to be within an interval related to the number of samples and the signal-to-noise ratio. By a numerical analysis, the theoretical results are shown to be also valid for the uniform noise model of quantization. Index Terms—IEEE Standards 1057 and 1251, model-order selection, sine-wave fit, waveform fit.

[1]  Peter Händel,et al.  Multiple-tone estimation by IEEE standard 1057 and the expectation-maximization algorithm , 2005, IEEE Transactions on Instrumentation and Measurement.

[2]  Arye Nehorai,et al.  Adaptive comb filtering for harmonic signal enhancement , 1986, IEEE Trans. Acoust. Speech Signal Process..

[3]  J. Blair.  Sine-fitting software for IEEE Standards 1057 and 1241 , 1999, IMTC/99. Proceedings of the 16th IEEE Instrumentation and Measurement Technology Conference (Cat. No.99CH36309).

[4]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[5]  István Kollár,et al.  Four-parameter fitting of sine wave testing result: iteration and convergence , 2004, Comput. Stand. Interfaces.

[6]  I. Kollar,et al.  Standard framework for IEEE-STD-1241 in MATLAB [ADC testing] , 2001, IMTC 2001. Proceedings of the 18th IEEE Instrumentation and Measurement Technology Conference. Rediscovering Measurement in the Age of Informatics (Cat. No.01CH 37188).

[7]  Andrzej Pacut,et al.  Effective resolution of analog to digital converters , 2003 .

[8]  Pasquale Arpaia,et al.  A critical note to IEEE 1057-94 standard on hysteretic ADC dynamic testing , 2001, IEEE Trans. Instrum. Meas..

[9]  Peter Händel,et al.  Properties of the IEEE-STD-1057 four-parameter sine wave fit algorithm , 2000, IEEE Trans. Instrum. Meas..

[10]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[11]  István Kollár,et al.  Improved determination of the best fitting sine wave in ADC testing , 2004, Proceedings of the 21st IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No.04CH37510).

[12]  Rik Pintelon,et al.  An improved sine-wave fitting procedure for characterizing data acquisition channels , 1995 .