An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform
An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform
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DOI：
10.1142/s0219691319500309
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Hua Yi;Peichang Ouyang;Tao Yu-;Tao Zhang
中科院分区：
文献类型：
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作者：
Hua Yi;Peichang Ouyang;Tao Yu-;Tao Zhang
连续小波变换（CWT）是信号与小波函数在固定尺度上的线性卷积。研究了以Morlet小波为母小波，采用非零填充线性卷积的连续小波变换算法。时域滤波器是小波函数的样本，是一种非因果滤波器。通过对该滤波器进行广义离散傅里叶变换（GDFT）和逆变换，可以得到该滤波器在其原始支撑外求值时的几何加权周期扩张。从时域滤波器的这种扩展，我们可以得到因果滤波器。本文利用该因果滤波器构造了基于GDFT的连续小波变换算法，该算法比Jorge Martinez提出的线性卷积算法形式更简洁。本文推导了该滤波器的GDFT的解析表达式，这是基于GDFT的连续小波变换算法所必需的。数值实验表明，基于GDFT的算法计算结果稳定可靠，运行速度快于其他两种算法。
Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work.