巴特沃斯小波构造与应用研究

Research on Construction and Application of Butterworth Wavelet

讨论了小波与正交滤波器组的相互构造关系 ,以及由正交滤波器组构造小波所要满足的正规性条件 .分析比较了由有限冲激响应 (FIR)滤波器组构造出的小波与无限冲激响应 (IIR)滤波器组构造出的小波 ,将基于IIR滤波器组的 7阶巴特沃斯小波与基于FIR滤波器组的Daubechies小波在信号降噪中的效果进行了比较 ,得出了低阶IIR滤波器组构造的小波可以与高阶FIR滤波器组构造出的小波分析效果相似 .证明Daubechies小波作为小波变换应用的一个分支 ,可以在数字信号处理中得到良好的应用 .

The inter-construction of wavelets and orthogonal filter banks is introduced, in which the orthogonal filter banks must be regular for constructing wavelets. The wavelets constructed respectively by FIR (finite impulse response) filter banks and IIR (infinite impulse response) filter banks are compared. The de-noise results of seven- order Butterworth wavelet (based on IIR filter banks) and Daubechies wavelet (based on FIR filter banks) are analyzed respectively. It shows that the result of low order IRR filter banks is similar to that of high order IFR filter banks. This proves that, as an embranchment of wavelet, Butterworth wavelet can be well applied in a digital signal processing.