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

Morlet and Gabor wavelet transforms are widely used in signal processing and image processing. In order to reduce its calculation time, we propose two types of calculation methods for Morlet wavelet transforms using the sliding Fourier transform (SFT). We also propose an algorithm to calculate SFT using the kernel integral on graphic processing unit (GPU). When the number of calculation cores in GPU is not less than the data size, the order of its calculation time is the logarithm of the smoothing size and does not depend on the data size. Using experiments, we compare the two methods for calculating the Morlet wavelet transform and evaluate the calculation time of the proposed algorithm using a kernel integral on GPU. For example, when the data size and the standard deviation are 102400 and 8192.0, respectively, the calculation time of the Morlet wavelet transform by the proposed method is 0.545 ms, which 413.6 times faster than a conventional method