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讨论了由正交滤波器组构造小波的方法和所要满足的正则性条件。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。并将基于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。最后,将巴特沃斯小波用于内燃机故障的诊断。证明巴特沃斯小波作为小波变换应用里的一个分支,可以在数字信号处理和故障诊断中得到良好的应用。
The method of constructing wavelet from orthogonal filter banks and the conditions of regularity to be satisfied are discussed. The wavelet constructed by the FIR filter bank and the infinite impulse response (IIR) filter bank are compared and analyzed. And compared the effects of 7th-order Butterworth wavelet based on IIR filter bank and Daubechies wavelet-based FIR filter bank in signal denoising, the conclusion is that low-order IIR filter bank can be constructed with high-order FIR Wavelet analysis constructed by the filter bank is similar. Finally, Butterworth wavelet is used to diagnose internal combustion engine faults. It is proved that Butterworth wavelet is a branch of wavelet transform application and can be well applied in digital signal processing and fault diagnosis.