16 bit量化误差对正弦参数拟合影响的误差界

为了定量评估量化采样序列对四参数正弦拟合结果影响的误差规律，针对16 bit量化对四参数正弦拟合带来的影响，分别在有效位数、幅度、频率、初始相位和直流分量五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，获得了各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。以往的研究仅使用正态随机噪声方式表征其谐波失真以外的误差要素，本文揭示了量化误差影响的周期性特征，并以曲线包络方式给出了量化误差影响的误差界。量化误差对四参数拟合影响的误差界，可用于不确定度估计，以及测量条件选择。

Error Bounds for the Influence of 16 bit Quantization Error on Sinusoidal Parameter Fitting

In order to quantitatively evaluate the error law of the influence of quantization sampling sequence on four parameter sinusoidal fitting results,aiming at the influence of 16 bit quantization on four parameter sinusoidal fitting,the fitting error bounds are searched on the five parameters of effective number of bits,amplitude,frequency,initial phase and DC component respectively.The selected conditional variables are amplitude,cycle number of waveform contained in the sequence,initial phase,DC component and number of sequence data points.The error bound search is carried out in the double condition combination mode of pairwise linkage,and the curve law of the error bound of various parameters changing with different conditions is obtained.The significant influence quantity and insignificant influence quantity,as well as the clear upper and lower bounds of the error are screened out.Previous studies only use normal random noise to characterize the error elements other than harmonic distortion,this paper reveals the periodic characteristics of the influence of quantization error,and give the error bound of the influence of quantization error in the form of curve envelope.The error bound of the influence of quantization error on four parameter fitting can be used for uncertainty estimation and measurement condition selection.