[PDF][PDF] Approximations using Hilbert transform of wavelets
Journal of Classical Analysis, 2015•researchgate.net
Hilbert transform of wavelets has been used to approximate functions in L2 (R). It is proved
that Hilbert transform of wavelets with many vanishing moments does a good job in
approximating smooth functions in L2 (R). We also prove that Hölder continuity of a function
helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we
give a result that relates the Hilbert transform of wavelet with dyadic scale differential
operator and use it to decrease the wavelet coefficients.
that Hilbert transform of wavelets with many vanishing moments does a good job in
approximating smooth functions in L2 (R). We also prove that Hölder continuity of a function
helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we
give a result that relates the Hilbert transform of wavelet with dyadic scale differential
operator and use it to decrease the wavelet coefficients.
Abstract
Hilbert transform of wavelets has been used to approximate functions in L2 (R). It is proved that Hilbert transform of wavelets with many vanishing moments does a good job in approximating smooth functions in L2 (R). We also prove that Hölder continuity of a function helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we give a result that relates the Hilbert transform of wavelet with dyadic scale differential operator and use it to decrease the wavelet coefficients.
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