基于离散傅里叶变换的频谱分析新方法

摘要

针对现有的测频算法和频谱分析方法还存在一些不足之处,提出了基于离散傅里叶变换的频谱分析新方法,它能准确计算出信号中的基频分量,整次谐波和非整次谐波的幅值,频率和相角,以及衰减直流分量的幅值和衰减时间常数.公式推导的过程先从简单的单信号模型入手,得到单个余弦信号的幅值、频率和相角,再推广到一般情况下的复杂信号,采用牛拉法迭代求解.算法精度高,不受初始采样点、采样频率和阶数的影响,实时性强.最后对具体算例进行仿真,所得结果验证了算法的正确性.%There are some shortcomings existing in present frequency measurement algorithm and spectrum analysis method. So a new method of spectrum analysis based on DFT is proposed, which can accurately calculate the fundamental component of signals,the amplitude, frequency and phase angle of integral harmonics and non-integral harmonics fundamental frequency component, and the amplitude and decay time constant of the decaying DC component. The deduction of formula starts from the model of a single signal to get the amplitude, frequency and phase angle of single cosine signal, then extends to the general complicated signal, using Newton-Raphson to solve the equations. The algorithm has the advantages of higher accuracy and stronger real-time. Besides, the influence of initial sampling point, frequency of sampling and order number is very small. The presented method is tested by specific example and the solution proves the validity of the method.