• Corpus ID: 239616413

Morlet wavelet transform using attenuated sliding Fourier transform and kernel integral for graphic processing unit

@article{Yamashita2021MorletWT,
  title={Morlet wavelet transform using attenuated sliding Fourier transform and kernel integral for graphic processing unit},
  author={Yukihiko Yamashita and Toru Wakahara},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.11866}
}
Morlet or Gabor wavelet transforms as well as Gaussian smoothing, are widely used in signal processing and image processing. However, the computational complexity of their direct calculations is proportional not only to the number of data points in a signal but also to the smoothing size, which is the standard deviation in the Gaussian function in their transform functions. Thus, when the standard deviation is large, its considerable computation time diminishes the advantages of aforementioned… 

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SHOWING 1-10 OF 27 REFERENCES
An algorithm for Morlet wavelet transform based on generalized discrete Fourier transform
TLDR
The algorithm of CWT with Morlet wavelet as mother wavelet is studied with a linear convolution of signal and wavelet function for a fixed scale.
Stabilized Calculation of Gaussian Smoothing and Its Differentials Using Attenuated Sliding Fourier Transform
TLDR
This work proposes the attenuated SFT (ASFT) by introducing a decay factor to the original SFT together with a new criterion for determining coefficients to effectively approximate Gaussian function and its differentials.
High Precision Computation of Morlet Wavelet Transform for Multi-period Analysis of Climate Data ⋆
TLDR
The algorithm proposed in this paper is free of shortcomings of FFT-based method and its precision is the best among existing linear-convolution-based methods.
Acceleration of Gaussian Filter with Short Window Length Using DCT-1
TLDR
Experiments show that the method overcomes naive Gaussian convolution and existing $O(1)$ GF in terms of computational time and, without truncating negligible terms, the method runs faster than convolution.
Cosine integral images for fast spatial and range filtering
Non uniform kernels is important for many image processing algorithms. However, for large kernel sizes the filtering can become computationally expensive. We introduce cosine integral images (CII)
A better way to define and describe Morlet wavelets for time-frequency analysis
TLDR
This paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (as full-width at half-maximum).
Universal Approach for DCT-Based Constant-Time Gaussian Filter with Moment Preservation
TLDR
Experiments found that DCT-7 shows the highest approximate accuracy, which is a new conclusion different from existing methods, and a closed-form solution to optimize weight coefficients is also proposed based on a simple convex analysis.
An algorithm for the machine calculation of complex Fourier series
TLDR
Good generalized these methods and gave elegant algorithms for which one class of applications is the calculation of Fourier series, applicable to certain problems in which one must multiply an N-vector by an N X N matrix which can be factored into m sparse matrices.
Feature Extraction Based on Morlet Wavelet and its Application for Mechanical Fault Diagnosis
Abstract The vibration signals of a machine always carry the dynamic information of the machine. These signals are very useful for the feature extraction and fault diagnosis. However, in many cases,
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