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2016•Unpublished venueRequires access

Wavelets and Continuous Wavelet Transform

Jasmina Veta Buralieva

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Abstract

The concepts of wavelet theory were provided by Meyer, Mallat, Daubechies and many others.Wavelets are well localized, oscillatory functions which provide a basis of and can be modified to a basis of , where is a bounded domain. Wavelet transform or wavelet analysis is a recently developed mathematical tool for signal analysis. In this paper are shown some relation for the wavelet transform and using Wolfram Mathematica 10 is given the wavelet transform of the signal . A prove that multiplication of real number with wavelet and sum of two wavelets are wavelets is also provided.

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What this paper is about

The concepts of wavelet theory were provided by Meyer, Mallat, Daubechies and many others.Wavelets are well localized, oscillatory functions which provide a basis of and can be modified to a basis of , where is a bounded domain. Wavelet transform or wavelet analysis is a recently developed mathematical tool for signal analysis. In this paper are shown some relation for the wavelet transform and using Wolfram Mathematica 10 is given the wavelet transform of the signal . A prove that multiplication of real number with wavelet and sum of two wavelets are wavelets is also provided.

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Available abstract

The concepts of wavelet theory were provided by Meyer, Mallat, Daubechies and many others.Wavelets are well localized, oscillatory functions which provide a basis of and can be modified to a basis of , where is a bounded domain. Wavelet transform or wavelet analysis is a recently developed mathematical tool for signal analysis. In this paper are shown some relation for the wavelet transform and using Wolfram Mathematica 10 is given the wavelet transform of the signal . A prove that multiplication of real number with wavelet and sum of two wavelets are wavelets is also provided.

Key concepts: Wavelet, Second-generation wavelet transform, Discrete wavelet transform, Stationary wavelet transform, Wavelet packet decomposition, Wavelet transform, Lifting scheme, Harmonic wavelet transform

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