一种基于等效采样的周期信号谐波分析方法

Harmonic Analysis Method of Periodic Signal based on Equivalent Sampling

为了突破周期信号谐波分析中采样保持与模数转换时间对分析信号频率范围的限制,将准均匀采样与等效采样相结合,提出了一种新的等效采样周期信号谐波分析方法。首先,给出了在奇数个信号周期内进行2的整数次方次均匀采样的等效采样谐波分析理论;其次,计入定时时钟周期对采样时间的影响,在等效采样中结合准均匀采样以实现同步采样;进一步分析了采样过程中的时间离散与幅值量化所带来的谐波分析误差;最后,给出了新的等效采样谐波分析的具体算法。借助含有小幅谐波分量的实验信号对等效采样谐波分析算法进行了数值仿真。理论分析和数值仿真均表明:新方法有效拓宽了分析信号的频率范围,并且可直接利用FFT进行快速计算。

In order to break through the limitation of sampling⁃hold and analog⁃to⁃digital conversion time on the frequency range of the analyzed signal in the harmonic analysis of periodic signals,a new harmonic analysis method for periodic signals is proposed by integrating quasi⁃uniform sampling into equivalent sampling.Firstly,the equivalent sampling harmonic analysis theory of integer power of 2 uniform samplings in odd signal periods is given;Secondly,considering the influence of timing clock cycle on sampling time,quasi⁃uniform sampling is integrated into equivalent sampling to achieve synchronous sampling;The harmonic analysis error caused by time discretization and amplitude quantization in the sampling process is further analyzed;Finally,the specific algorithm of the new equivalent sampling harmonic analysis method is given.Based on the experimental signal with small amplitude harmonic components,the equivalent sampling harmonic analysis algorithm is numerically simulated.Theoretical analysis and numerical simulation show that the new method effectively expands the frequency range of the analyzed signal,and can directly use FFT for fast calculation.