【摘要】 谐和小波和广义谐和小波皆为在频域上紧支且时域为无穷的正交小波,其频域分辨率很好但时域分辨率较差。虽然谐和小波在无穷时域上具有正交性,但其正交性在有限时域上却无法体现。针对这个缺点,在广义谐和小波的基础上,将广义谐和小波周期化后,进而提出了一种周期广义谐和小波(Periodic Generalized Harmonic Wavelet,PGHW)。PGHW的母小波在时域中可以表达为经平移后的若干谐和项之和,在频域中表现若干δ函数之和,为一种以待分析信号持时为基本周期且在其上正交的离散广义谐和小波。基于PGHW在频域内的简单性,利用快速Fourier变换(FFT)技术实现了PGHW的快速小波变换及逆变换。最后的算例给出了某人工合成地震波的周期广义谐和小波变换及其重构,说明了所提算法的高效性与PGHW的完全重构性。更多还原

【Abstract】 The periodic generalized harmonic wavelet(PGHW) and the algorithms for its fast wavelet transformation(FWT) and inverse fast wavelet transformation(iFWT) are presented here.The PGHW can be represented as a sum of several translated harmonic terms in time domain,and a sum of several δ functions in frequency domain.Compared to the generalized harmonic wavelet(GHW) and the harmonic wavelet(HW),the PGHW is orthogonal and periodic,while the former lose the orthogonality in a finite time interval.Considering the simplicity of the PGHW in frequency domain,its FWT and iFWT are developed via the fast Fourier transformation(FFT) technique.Numerical examples demonstrated the computational efficiency of the algorithms and the perfect reconstruction of the PGHW.更多还原