一种基于定尺度小波变换的频率估计算法

A Frequency Estimation Algorithm Based on Fixed Scale Wavelet Transform

通过改变尺度实现频率扫描是基于小波变换的频率估计算法的惯常做法。由于小波参数的确定缺乏具体明确的方法,这种做法在实际应用中很难达到其算法的理论最佳性能。针对这一问题,首先通过详细推导组合复Morlet小波变换与待分析信号傅里叶变换的关系,提出了一种基于定尺度小波变换的频率估计算法;然后讨论了控制频谱混叠、保证估计精度及分辨能力的参数设置问题,提出了一种简单易行的设置方法。仿真分析表明,该方法进行频率估计在混叠对抗及噪声抑制方面具有比FFT算法明显更优的性能,且适用于短数据信号。

By changing the scale to realize frequency scanning is usual practice in frequency estimation algo-rithms based on wavelet transform. As a result of lack of specific method to determine the wavelet parameters, inpractice theoretical optimal performances of the algorithms are difficult to achieve by this approach. Aiming at thisproblem, first a kind of frequency estimation algorithm based on fixed scale wavelet transform is put forwardthroughdetailed calculation of the relationship between the combined complex Morlet wavelet transform and Fourier trans-form of the signals to be analyzed. After that the matter of spectrum aliasing control to ensure estimation precisionand resolution is discussed and a simple parameters setting method is proposed. On the basis of simulation analysis,significantly better performances in aliasing resistance and noise suppression than that of FFT algorithm as well asapplicability for short-data signals are indicated by using this method for frequency estimation.