基于连续小波变换的非整数次谐波测量方法

快速傅里叶变换(FFT)可实现整数次谐波的精确检测，但对非整数次谐波的检测误差较大；加窗插值算法可提高非整数次谐波的检测精度，但会导致谐波分辨率降低。如果信号中存在频率相近的整数次和非整数次谐波，利用FFT和加窗插值算法都无法实现谐波的准确检测。连续小波变换(CWT)因其良好的时频局部化特性，可用来分析谐波。通常利用CWT系数的幅值来检测谐波频率。但不同尺度的小波函数在频域上存在相互干扰，如果被检测信号中含有频率相近的谐波，利用CWT系数的幅值无法实现谐波的准确检测。文中结合傅里叶变换和CWT的特点，提出了利用小波变换系数傅里叶变换的幅值来分离谐波的算法。通过实例验证，该算法能够把频率相近的整数次和非整数次谐波分离，实现较理想的检测，从而提高了谐波分析、检测的精度。

A NOVEL METHOD FOR NON-INTEGER HARMONICS MEASUREMENT USING CONTINUOUS WAVELET TRANSFORM

Fast Fourier transform (FFT) can measure integer harmonics precisely, but with great error for non-integer harmonics. The interpolating windowed FFT can improve measurement precision of non-integer harmonics, while resulting in low resolution. For a signal containing several integer and non-integer harmonics with near frequency, both the existing FFT methods and interpolating algorithms cannot solve it with satisfaction. The continuous wavelet transform (CWT) has been used to measure harmonics due to its excellent time-frequency character. The usual method is to measure the harmonic frequency according to the amplitude of the CWT coefficients, but the wavelet function with different scales often disturb each other in frequency domain. If the measured harmonics contain the near frequency ones, they cannot be measured accurately. So the paper presents a scale-FFT magnitude method to separate integer and non-integer harmonics combining FFT with CWT. Simulations further validate the accuracy of the presented method, thus improving the precision of harmonic detection.