Abstract：The running time of the four-parameter sine wave curve fitting software is studied, and a quantitative evaluation method of the software fitting time is proposed. The influence of the time used for the four-parameter sinusoidal curve fitting is quantitatively evaluated on the different factors and conditions such as the length of the sequence, the number of signal cycles contained in the sequence, the amplitude of the sine wave, the phase, the DC component, and the number of A/D bits, and the law of the fitting time varying versus each factor is obtained. Aiming at the main factors affecting the software running time, a fast fitting method is proposed to reduce the fitting time by reducing the length of the fitting sequence. They are direct sequence interception method and secondary sampling method. The validity and feasibility of the method are verified by a group of experiments, the conclusion is that the secondary sampling method is superior to the direct interception method. Both of them all can be used for fast calculation of four-parameter sine fitting.
IEEE Standard for Terminology and Test Methods for Analog-to-Digital Converters: IEEE Std 1241-2010［S］. 2010.
YUAN X F, XU H L, CHEN S H.A Simplex-method-Based Algorithm for Calculating Waveform Parameters of Sine Wave ［J］. Electronic Measurement Technology, 2004 (1): 13-14.
JENG Y C, CROSBY P B. Sinewave Parameter Estimation Algorithm with Application to Waveform Digitizer Effective Bits Measurement ［J］. IEEE Transactions on Instrumentation and Measurement, 1988, 37 (4): 529-532.
［2］
PINTELON R, SCHOUKENS J. An improved sine-wave fitting procedure for characterizing data acquisition channels ［J］. IEEE Transactions on Instrumentation & Measurement, 1996, 45 (2): 588-593.
ZHU S Y, ZENG T, LONG T.An Improved Sine Fitting Test for the Data Acquisition System ［J］. Transactions of Beijing Institute of Technology, 2000, 20 (6): 757-761.
XU H L, YUAN X F, CHEN S H. Hybrid Optimization Algorithm for Curve-fit Model of Sinusoid Wave Parameters ［J］. Journal of Electronic Measurement and Instrument, 2004, 18 (4): 1-5.
［6］
SILVA M, RAMOS P M, SERRA A C. A new four parameter sine fitting technique ［J］. Measurement, 2004, 35 (2): 131-137.
［8］
KOLLAR I, BLAIR J J. Improved determination of the best fitting sine wave in ADC testing ［J］. IEEE Transactions on Instrumentation & Measurement, 2005, 54 (5): 1978-1983.
SU D L, WANG S C, ZHANG A J. Four-parameter Sine Wave Curve-fit Based on Genetic Algorithms ［J］. Metrology & Measurement Technology, 2005, 25 (6): 18-20.
TIAN S P, WANG J, YAN D T, et al. Extraction of Sinusoidal Parameter Based on Genetic Algorithm ［J］. Measurement Technique, 2005, (5): 3-5.
［17］
CHEN K F. Estimating Parameters of a Sine Wave by Separable Nonlinear Least Squares Fitting ［J］. IEEE Transactions on Instrumentation & Measurement, 2010, 59 (12): 3214-3217.
LIANG Z G.The four-parameter sinusoidal curve-fit method by using combination methods ［J］. Acta Metrologica Sinica, 2021, 42 (12): 1559-1566.
LIANG Z G, WU T F, ZHANG D P, et al.The Influence of SNR of Waveforms to Sinusoidal Curve-fit in Partial Period ［J］. Acta Metrologica Sinica, 2013, 34 (5): 474-479.
LIANG Z G.The improvement and experiment analysis for a four-parameter sine wave curve-fit method ［J］. Acta Metrologica Sinica, 2017, 38 (4): 492-498.
［26］
H?NDEL P. Amplitude estimation using IEEE-STD-1057 three-parameter sine wave fit: Statistical distribution, bias and variance ［J］. Measurement, 2010, 43 (6): 766-770.
［29］
BELEGA D, PETRI D. Cramér-Rao Lower Bound for Unbiased Estimators of Sampled Noisy Sine-Wave Parameters ［J］. IEEE Transactions on Instrumentation and Measurement, 2021, 70: 1010809.
［31］
McCOMB T R, KUFFEL J, Le ROUX B C. A Comparative Evaluation of Some Practical Algorithms Used in the Effective Bits Test of Waveform Recorders ［J］. IEEE Transactions on Instrumentation and Measurement, 1989, 38 (1): 37-42.
LIANG Z G, ZHU J J, MENG X F.Convergence algorithm of four-parameter sine wave curve-fit ［J］. Chinese Journal of Scientific Instrument, 2006, 27 (11): 1513-1519.
WU Y H, YANG J F, CHENG J Y, et al. High-accuracy estimation algorithm for 4 parameters of sine-wave ［J］. Journal of University of Science and Technology of China, 2006, 36 (6): 625-629.
［16］
Performance characteristics and calibration methods for digital data acquisition systems and relevant software: IEC 62008-2005［S］. 2005.
ZHANG J Q, ZHAO X M, HU X, et al.Sine wave fit algorithm based on total least-squares method with application to ADC effective bits measurement ［J］. IEEE transactions on Instrumentation and Measurement, 1997, 46 (4): 1026-1030.
LIANG Z G, ZHANG D Z, SUN J Y, et al.A Fast Arithmetic Method of Four-parameter Sine Wave Curve fit ［J］. Metrology & Measurement Technology, Feb. 2006, 21 (1): 4-7.
［30］
KUFFEL J, McCOMB T R, MALEWSKI R. Comparative Evaluation of Computer Methods for Calculating the Best-Fit Sinusoid to the Digital Record of a High-Purity Sine Wave ［J］. IEEE Transactions on Instrumentation and Measurement, 1987, 36 (3): 418-422.
［7］
BILAU T Z, MEGYERI T, SRHEGYI A, et al. Four-parameter fitting of sine wave testing result: iteration and convergence ［J］. Computer Standards & Interfaces, 2004, 26 (1): 51-56.
［13］
TREES H, BELL K L. Single Tone Parameter Estimation from Discrete Time Observations［M］. Wiley-IEEE Press, 2009.
LIANG Z G.The sinewave fit algorithm based on total least-square method with partial period waveforms and non-uniform sampling ［J］. Acta Metrologica Sinica, 2021, 42 (3): 358-364.
［27］
RENCZES B, I KOLLR, MOSCHITTA A, et al. Numerical Optimization Problems of Sine-Wave Fitting Algorithms in the Presence of Roundoff Errors ［J］. IEEE Transactions on Instrumentation & Measurement, 2016, 65 (8): 1785-1795.
LIANG Z G, MENG X F.A Curve-fit Arithmetic of Four-parameter Sine Wave for Partial Period ［J］. Acta Metrologica Sinica, 2009, 30 (3): 245-249.
DEYST J P, SOULDERS T M, SOLOMON O M. Bounds on Least-Squares Four-Parameter Sine-Fit Errors Due to Harmonic Distortion and Noise ［J］. IEEE Transaction on Instrumentation & Measurement, 1995, 44 (3): 637-642.
［28］
NEGUSSE S, HANDEL P, ZETTERBERG P. IEEE-STD-1057 Three Parameter Sine Wave Fit for SNR Estimation: Performance Analysis and Alternative Estimators ［J］. IEEE Transactions on Instrumentation & Measurement, 2014, 63 (6): 1514-1523.
2024, Vol. 45 
