利用Morlet连续小波变换实现非整次谐波的检测

针对常规快速傅立叶变换无法检测非整次谐波的问题。文章提出了利用小波变换实现检测非整次谐波的方法。小波函数是具有时域和频域良好局部化特性的函数，理论上可以用于非整次谐波的检测，但是小波变换存在着由于频谱泄露而带来的混频问题，给谐波的检测带来误差。为解决此问题，可选择分频严格的小波函数，或者选择合适的分析方法，该文选用的分析方法是连续小波变换，选用的基小波是具有良好频域特性的Morlet小波，通过Matlab仿真，在1个周期的采样数据中，能够较为准确地把不同频率的整次和非整次谐波分离出来，这表明了小波变换对于非整次谐波的检测和分析是可行的，从而为谐波的精确检测提供了有效的手段。

MORLET WAVELET BASED DETECTION OF NONINTEGER HARMONICS

For the problem that the non-integer harmonic cannot be detected by FFT transformation, a non-integer harmonics detection method is implemented by a wavelet based transformation (WT) method. The wavelet function is such a function which possesses good localization characteristics, so theoretically it can be applied to the detection of non-integer harmonics. Because of the frequency mixing phenomenon caused by leakage of frequency spectrum some errors are brought to the detection of harmonics. To solve this problem there are two aspects which should be paid attention to: one is to choose a wavelet function which can strictly carry out the frequency division and the another is to choose a suitable frequency division method. In this paper the Morlet wavelet which possesses good frequency domain characteristics is chosen. The analyzing method used in this paper is continuous wavelet transformation and the Morlet wavelet with good frequency domain characteristics is chosen as base wavelet. Through the simulation with MATLAB the integer and non-integer harmonics with different frequencies can be more accurately separated from the sampled data during one period. It proves that it is feasible to apply the wavelet transformation to the detection of non-integer harmonics, thus, an effective means is provided for accurate detection of harmonics.