Close expressions for Meyer Wavelet and Scale Function
V.VV. Vermehren, H.M. de Oliveira
TL;DR
This paper derives new explicit analytical expressions for the Meyer wavelet and scale function, enabling exact time-domain representations and facilitating practical computations without approximation errors.
Contribution
It introduces straightforward analytical formulas for Meyer wavelet and scale functions, previously only defined in the frequency domain.
Findings
Derived exact time-domain expressions for Meyer wavelet and scale function.
Validated formulas through numerical computations with no approximation error.
Enhances practical applications of Meyer wavelet in signal processing.
Abstract
Many continuous wavelets are defined in the frequency domain and do not have analytical expressions in the time domain. Meyer wavelet is ordinarily defined in this way. In this note, we derive new straightforward analytical expressions for both the wavelet and scale function for the Meyer basis. The validity of these expressions is corroborated by numerical computations, yielding no approximation error.
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