论文部分内容阅读
为减小频谱泄漏对谱分析的影响,将传统离散傅里叶变换(DFT:Discrete Fourier Transform)的方法和运算从经典的一维频谱扩展到二维时频谱,在此基础上对简谐信号存在能量泄漏的频谱中任意频率成分的幅值与时域信号截断长度的关系(时谱)进行实验研究,从而提出一种信号的时谱描述方法。实验结果表明,在频谱泄漏条件下任意频率成分的幅值随时域信号截断长度的变化遵从︱sinc︱函数,基于这种关系可完成简谐信号任意截断条件下的频谱构造,实现零误差幅值谱构成,得到非整周期截断时DFT幅值谱误差与信号中所含周期数的关系服从指数规律,且当信号长度是周期的10倍时,DFT频谱产生的标准差约为0.001。
In order to reduce the influence of spectral leakage on spectral analysis, the traditional methods and operations of Discrete Fourier Transform (DFT) are expanded from classical one-dimensional spectrum to two-dimensional time-frequency spectrum. Based on this, The relationship between the amplitude of any frequency component in the spectrum of energy leakage and the truncation length of the time domain signal (time-frequency spectrum) is studied experimentally, and a time-spectrum description method of the signal is proposed. The experimental results show that the amplitude of arbitrary frequency component under the condition of spectral leakage changes with the time-domain signal truncation length follows the function of ︱incinc, Based on this relationship can be completed under arbitrary truncation of the harmonic signal spectral structure, to achieve zero error amplitude The relationship between the DFT amplitude spectrum error and the number of periods contained in the signal follows the exponential law and the standard deviation of the DFT spectrum is about 0.001 when the signal length is ten times of the period.