6533b859fe1ef96bd12b753b

RESEARCH PRODUCT

Periodic Orthogonal Wavelets and Wavelet Packets

Amir AverbuchValery A. ZheludevValery A. ZheludevPekka Neittaanmäki

subject

Spline (mathematics)WaveletComputer scienceNetwork packetFast Fourier transformComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONMathematicsofComputing_NUMERICALANALYSISData_CODINGANDINFORMATIONTHEORYTime domainVanishing momentsNyquist frequencyAlgorithmWavelet packet decomposition

description

In this chapter, we discuss how to derive versatile families of periodic discrete-time orthogonal wavelets and wavelet packets from discrete and discrete-time splines outlined in Chap. 3. These wavelets and wavelet packets, although not having compact supports, are well localized in the time domain. They can have any number of discrete vanishing moments. Their DFT spectra tend to have a rectangular shape when the spline order grows and provide a collection of refined splits of the Nyquist frequency band. The wavelet and wavelet packet transforms are implemented in a fast way using the FFT.

yearjournalcountryeditionlanguage
2018-06-20
https://doi.org/10.1007/978-3-319-92123-5_4