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本文简要地介绍了信号的时-频两维分析的目的、意义,分析对比了小波分析和短时富里叶分析、Wigner 谱分析的异同及主要优点。简述了离散小波变换、离散二进小波变换和离散二进正交小波变换的数字实现方法。文中详细论述了反对称小波和对称小波两类不同小波函数的性质及对小波变换的影响,并分析了它们在异常信号检测中的不同作用。最后介绍了离散二进小波变换滤波器的设计方法,给出了小波互补滤波器的幅频特性公式,并列举了两个滤波器设计实例。
This paper briefly introduces the purpose and significance of time-frequency two-dimensional analysis of signals, analyzes and compares the similarities and differences and main advantages of wavelet analysis and short-time Fourier analysis and Wigner spectrum analysis. The digital realization methods of discrete wavelet transform, discrete binary wavelet transform and discrete binary orthogonal wavelet transform are briefly introduced. In this paper, the properties of two kinds of different wavelet functions of antisymmetric and symmetric wavelets and their influence on wavelet transform are discussed in detail, and their different roles in abnormal signal detection are analyzed. Finally, the design method of discrete binary wavelet transform filter is introduced. The amplitude-frequency characteristic formula of wavelet complementary filter is given. Two filter design examples are given.