6533b82ffe1ef96bd1296500

RESEARCH PRODUCT

Biorthogonal Wavelet Transforms Originating from Discrete and Discrete-Time Splines

Valery A. ZheludevValery A. ZheludevAmir AverbuchPekka Neittaanmäki

subject

Pure mathematicsWaveletLifting schemeDiscrete time and continuous timeFast Fourier transformImage processingFilter (signal processing)Time domainBiorthogonal waveletMathematics

description

This chapter describes how to generate families of biorthogonal wavelet transforms in spaces of periodic signals using prediction p-filters originating from discrete-time and discrete splines. The transforms are generated by the lifting scheme (Sweldens (Wavelet applications in signal and image processing III, vol 2569, 1995, [7]), Sweldens (Appl Comput Harmon Anal 3:186–200, 1996, [8]), Sweldens (SIAM J Math Anal 29:511–546, 1997, [9]), see also Sect. 7.1 of this volume). The discrete-time wavelets related to those transforms are (anti)symmetric, well localized in time domain and have flat spectra. These families comprise wavelets with any number of local discrete vanishing moments (LDVMs). The transforms are implemented in a fast way using the FFT by critically sampled perfect reconstruction periodic filter banks.

yearjournalcountryeditionlanguage
2018-06-20
https://doi.org/10.1007/978-3-319-92123-5_8