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 one-dimensional integrations with respect to the scale parameter, and hence the continuous wavelet transforms constructed in this way are more ready to use than the usual scheme. We then apply the Gaussian-derived 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 continuous wavelet transforms. The transforms are very easy to perform, and we believe that the simplicity of our wavelet scheme will make continuous wavelet transforms very useful in practice.

9 Pages, 4 Figures, comments welcome

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Cited by in corpus (10)

• Comparisons between fast algorithms for the continuous wavelet transform and applications in cosmology: the 1D case
• Continuous wavelet analysis of matter clustering using the Gaussian-derived wavelet
• Simultaneous Dependence of Matter Clustering on Scale and Environment
• How do baryonic effects on the cosmic matter distribution vary with scale and local density environment?
• Capturing primordial non-Gaussian signatures in the late Universe by multi-scale extrema of the cosmic log-density field
• Turbulence revealed by wavelet transform: power spectrum and intermittency for the velocity field of the cosmic baryonic fluid
• Turbulence, Thermal Pressure, and Their Dynamical Effects on Cosmic Baryonic Fluid
• Identifying Halos in Cosmological Simulations with Continuous Wavelet Analysis: The 2D Case
• CWTHF: Identifying Dark Matter Halos with Continuous Wavelet Transform
• CWTHF: Subhalo Identification with Continuous Wavelet Transform