FFT算法截断不确定度评估

Truncation Uncertainty Evaluation of Fast Fourier Transform Algorithm

截断不确定度是快速傅里叶算法不确定度评估中的一个重要来源。将截断不确定度分解为频谱泄露不确定度、加窗和栅栏效应不确定度进行分析。将采样周期个数分解为整数部分和小数部分,确定小数部分引起的频谱泄露误差区间,以此为基础给出频谱泄露不确定度的评估方法;将加窗和栅栏效应引入的不确定度作为一个整体分析,避开分量之间的相关性,以三角窗为例给出了一个通用的评估方法。之后,利用GUM中的B类方法对其进行评定,评定时假设舍入测量不确定度为反正弦分布,并通过对频谱泄露不确定度、加窗和栅栏效应不确定度进行合成,得到最终的截断不确定度,在此基础上建立了FFT截断不确定度的通用评估方法。

Truncation uncertainty is an important source of the uncertainty evaluation for Fast Fourier Transform algorithm. The truncation uncertainty can be decomposed into the spectrum leakage uncertainty, the barrier affect and the window affect uncertainty. The sampling period is decomposed into the integer part and the fractional part, and the error interval of the spectrum leakage is determined. On the basis, the evaluation method of spectrum leakage can be given. The uncertainty of the window and the barrier effect is used as a whole to avoid the correlation between the two components, and a general evaluation method is presented for the case of a triangular window. Assuming truncation uncertainty distribution as arc-sine distribution, the spectrum leakage uncertainty, the window effect and the barrier effect uncertainty are synthesized. Finally it obtains the values of truncation uncertainty by type B evaluation of GUM, based on which, a unified method for the evaluation of the truncation uncertainty of FFT can be established.