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| Experimental Study on Fitting Sinusoidal Parameter Error Boundaries Resulting From Quantization |
| LIANG Zhi-guo |
| National Key Laboratory of Science and Technology on Metrology & Calibration, Changcheng Institute of Metrology and Measurement, Beijing 100095, China |
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Abstract When the sinusoidal waveform parameters legally estimated, the measurement conditions have the error of the fitting parameters to perform the search research. The selected condition variables are the number of A/D bits, the number of signal cycles in sampling sequence, and the sequence length. The error bounds variation versus conditions is performed, and the error bounds of the equipped parameters such as amplitude, frequency, phase, DC offset, and effective bits are obtained with different conditions change. And all of the effects about the number of A/D bits, the waveform cycles contained in the sequence, and the sequence length have been in-depth researched. The error sequence of the fitting parameters has a significant law of the quantified step characteristics as the sequence length change, the variation rules of quantified ladder width and height are given. For the same number of signal cycles in sampling sequence, the variation of each fitting parameter error as the quantum step sequence number m varies on 1/m2 regularity; for the quantization error step number m is constant, both the fit frequency error and the fitting phase error are varied according the signal cycles N in sampling sequence as of 1/N2 regularity. The errors of fitting amplitude, the fitting DC offset, and the effective bits have the same regularity, they are all will decrease as the number of signal cycles N increase. These results can be used to fit the error evaluation and uncertainty estimation of the sinusoidal parameter, or it can also be used to select measurement conditions in the case of setting fitting errors and uncertainties.
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Received: 09 March 2022
Published: 21 September 2023
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2023, Vol. 44 
