Morlet Wavelet Transform Using Sliding Fourier Transform and Kernel Integral for Graphic Processing Unit

2021 ◽  
Author(s):  
Yukihiko Yamashita ◽  
Toru Wakahara
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Graphic Processing Unit ◽  
Morlet Wavelet ◽  
Processing Unit ◽  
Morlet Wavelet Transform ◽  
Graphic Processing

An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform

2019 ◽  
Vol 17 (05) ◽  
pp. 1950030
Author(s):  
Hua Yi ◽  
Peichang Ouyang ◽  
Tao Yu ◽  
Tao Zhang
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Discrete Fourier Transform ◽  
Time Domain ◽  
Morlet Wavelet ◽  
Wavelet Function ◽  
Linear Convolution ◽  
Calculation Results ◽  
Morlet Wavelet Transform ◽  
The Time Domain

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.

339 Morlet wavelet transform in EEG during perceptuo-motor tasks

1998 ◽  
Vol 30 (1-2) ◽  
pp. 131-132
Author(s):  
S. Slobounovl ◽  
R. Tutwiler ◽  
E. Slobounova
Keyword(s):  
Wavelet Transform ◽  
Morlet Wavelet ◽  
Motor Tasks ◽  
Morlet Wavelet Transform
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