6533b827fe1ef96bd128649b

RESEARCH PRODUCT

Discrete Periodic Spline Wavelets and Wavelet Packets

Valery A. ZheludevPekka NeittaanmäkiAmir Averbuch

subject

Discrete wavelet transformPhysicsDiscrete mathematicsSpline (mathematics)symbols.namesakeWaveletFourier transformLifting schemeFast Fourier transformsymbolsInverseWavelet packet decomposition

description

Similarly to periodic polynomial splines, existence of the set of embedded discrete periodic splines spaces \(\varPi [N]= \fancyscript{S}_{[0]}\supset {}^{2r} \fancyscript{S}_{[1]}\supset \cdots \supset {}^{2r} \fancyscript{S}_{[m]}\cdots \), combined with the DSHA provides flexible tools for design and implementation of wavelet and wavelet packet transforms. As in the polynomial case, all the calculations consist of fast direct and inverse Fourier transforms (FFT and IFFT, respectively) and simple arithmetic operations. Raising the splines order does not increase the computation complexity.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-94-017-8926-4_14