Title :
Periodic shift-invariant multiresolution analysis
Author :
Bastys, Algirdas
Author_Institution :
Dept. of Math., Vilnius Univ., Lithuania
Abstract :
The Shannon multiresolution analysis and two methods of its periodization are considered. The class of all shift-invariant multiperiodic analyses with complex-valued scaling functions is described. All weakly shift-invariant periodic analogues of the Shannon scaling function are found. Among them, two shift-invariant periodic analogues of the sine function are revealed. A wavelet packet transform that generalizes the discrete Fourier transformation is found. An application of the shift-invariant periodic wavelet packet bases for time-frequency analysis of speech signals is discussed and illustrated
Keywords :
discrete Fourier transforms; information theory; signal resolution; speech processing; time-frequency analysis; time-varying systems; wavelet transforms; Shannon multiresolution analysis; Shannon scaling function; complex-valued scaling functions; discrete Fourier transformation; periodic shift-invariant multiresolution analysis; shift-invariant multiperiodic analysis; shift-invariant periodic wavelet packet bases; sine function; speech signal analysis; time-frequency analysis; wavelet packet transform; weakly shift-invariant periodic analogues; Extraterrestrial phenomena; Filters; Humans; Mathematics; Multiresolution analysis; Psychology; Sampling methods; Signal analysis; Spline; Visual system;
Conference_Titel :
Digital Signal Processing Workshop Proceedings, 1996., IEEE
Conference_Location :
Loen
Print_ISBN :
0-7803-3629-1
DOI :
10.1109/DSPWS.1996.555545