改进型小波多分辨率分析及小波梳状滤波器

Modified wavelet multiresolution analysis and novel wavelet comb filter

为克服小波多分辨率分析在高频段频率分辨率低的缺点,提出一种改进型小波多分辨率分析算法,并在此基础上给出一种新型小波梳状滤波器(WCF)的实现方法.改进型小波多分辨率分析算法对高频段进行逐级细分,得到一系列窄带的共轭正交滤波器(CQFs)及其输出信号序列.利用共轭正交滤波器的频率响应特性,将这些窄带滤波器通道组合成WCF.理论分析与仿真结果均表明,WCF在各频段都具有相同的频率分辨率,并能够检测子频带交界处的频率分量.WCF不仅易于实现,而且可以根据问题需要设定子带带宽,得到足够高的频率分辨率,适用于时变和非平稳信号时频特征的检测.

To overcome the wavelet multiresolution analysis's shortcoming of low resolution in high frequency bands, a modified wavelet multiresolution analysis algorithm and a novel wavelet comb filter (WCF) based on the modified algorithm were proposed. The modified wavelet multiresolution analysis algorithm subdivided the low frequency and high frequency bands into a series of narrow band conjugate quadrature filters (CQFs). By using their properties of the frequency responses, these CQFs can be combined into a WCF. Theoretical analysis and simulation results show that the novel WCF has identical frequency resolution in all frequency bands, and can detect the frequency components on the cross points of neighboring subbands. The novel WCF is convenient for implementation, and its subband bandwidth can be set according to the needs of different problems to obtain high enough frequency resolution. The WCF is suitable for the time-frequency characteristic detection of time-varying and non-stationary signals.