The continuous wavelet derived by smoothing function and its application in cosmology
Abstract
The wavelet analysis technique is a powerful tool and is widely used in broad disciplines of engineering, technology, and sciences. In this work, we present a novel scheme of constructing continuous wavelet functions, in which the wavelet functions are obtained by taking the first derivative of smoothing functions with respect to the scale parameter. Due to this wavelet constructing scheme, the inverse transforms are only onedimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms (CWTs) constructed in this way are more ready to use than the usual scheme. We then apply the Gaussianderived wavelet constructed by our scheme to computations of the density power spectrum for dark matter, the velocity power spectrum and the kinetic energy spectrum for baryonic fluid. These computations exhibit the convenience and strength of the CWTs. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make CWTs very useful in practice.
 Publication:

Communications in Theoretical Physics
 Pub Date:
 September 2021
 DOI:
 10.1088/15729494/ac10be
 arXiv:
 arXiv:2104.09505
 Bibcode:
 2021CoTPh..73i5402W
 Keywords:

 wavelet analysis;
 intergalactic medium;
 largescale structure of Universe;
 Astrophysics  Instrumentation and Methods for Astrophysics;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Physics  Computational Physics
 EPrint:
 9 Pages, 4 Figures, comments welcome