8 bit量化误差对正弦参数拟合影响的误差界

Bounds on Least-Squares Four-Parameter Sine-Fit Errors due to 8 bit Quantization

针对量化误差对四参数正弦拟合带来的误差影响,分别在有效位数、幅度、频率、初始相位和直流分量5项参数上进行了拟合误差界的搜索。选取的条件变量分别是幅度、序列所含波形的周波数、初始相位、直流分量以及序列数据点数。以两两联动的双条件组合方式进行误差界搜索,获得了上述5项参数的误差界随不同条件变化而变化的曲线规律,筛分出了显著影响量和不显著影响量,以及明确的误差上界和下界。该结果可用于拟合参数的误差和不确定度估计,也可以在设定拟合误差和不确定度情况下,选择测量条件。

Aiming at the influence of the quantization error on the four-parameter sinusoidal fitting error,the fitting error bounds were searched on the five parameters of effective bits,amplitude,frequency,initial phase and DC component.The selected condition variables were amplitude,the number of cycles of the waveform contained in the sequence,the initial phase,the DC component and the number of sequence data points.The error boundary search was carried out in a two-condition combination styles,and the error curves of the above five parameters were gained with each condition,including both the upper and the lower error bounds.The result can be used to estimate the error and uncertainty of the fitting parameters,or to construct the measurement conditions under the hoping fitting error and uncertainty.