工程信号处理中离散傅里叶变换的误差

离散傅里叶变换（DFT）的误差一般是通过窗函数的卷积来解释的，作者从内积运算诊断相关信号的观点，分析了DFT误差的原因，给出了误差公式，指出基向量和被分析信号的向量不吻合是造成内积运算诊断相关信号误差的根本原因．通过计算例子分析了DFr方法的误差特性：DFT分析结果在分析时间丁内插值细分，或延拓出分析时间T以外者时，存在误差；DFT分析结果会出现一定的随机性；DFT在快速逼近信号方面效率不高．分析时间长度丁对DFT分析的误差有影响：增加丁可以消减旁瓣误差，但是不能消减泄露误差．

Characterizing discrete Fourier transform errors in signal processing by inner product

Convolution of windowing function is traditionally used to explain the Discrete Fourier Transform(DFT) errors.In this work,the inner product of diagnosing correlation signals was used,and the equations of amplitude and phase errors were formulated.It is seen that the errors exist if the base vectors and the vectors of the analyzed signals are not in step.The example results show that errors occur when the DFT output is interpolated within the analyzing time T or when it is obtained beyond the time T.The DFT output may be random to a certain extent.The errors usually reduce the efficiency of convergence in the signal approximation.The analyzing time T has a large effect on the DFT analysis: increasing time T reduces the lobe errors,but may not reduce the leakage errors.