Integral and Discrete Transformations with Wavelet Theory

Course Description

Fourier analysis: series, transform and integral. The Laplace transform. The discrete transforms: DFT, FFT, and z-transform. The distributions: regular, delta and singular. Wavelet analysis: orthonormal bases, translation, dilatation and modulation, construction, examples. Hilbert spaces. Continuous Wavelet transform. Chirp: transform, series and oscillations. Applications: signal analysis, communication theory, data compression, differential equations.

Study Programmes

Postgraduate doctoral study programme

Literature

Stephane Jaffard, Yves Meyer, Robert D. Ryan (2001.), Wavelets, SIAM
M. Vetterli, J. Kovačević (2007.), Wavelets and Subband Coding, Prentice Hall PTR, Englewood Cliffs, New Jersey
Guangbin Ren, Qiuhui Chen, Paula Cerejeiras, Uwe Kaehle (2011.), Chirp transforms and chirp series, Journal of Mathematical Analysis and Applications, Vol. 373, No. 2, pp. 356-369
M. Pašić, S. Tanaka (2013.), Fractal oscillations of chirp functions and applications to second-order linear differential equations, International Journal of Differential Equations, Vol. 2013, Article ID 857410, 11 pp.
Yves Meyer, Hong Xu (1997.), Wavelet analysis and chirps, Applied and Computational Harmonic Analysis, Vol. 4, No. 4, pp. 366-379
Marián Képesi, Luis Weruaga (2006.), Adaptive chirp-based time-frequency analysis of speech signals, Speech Communication, Vol. 48, No. 5, pp. 474-492
Eugenio Hernandez, Guido Weiss (1996.), A First Course on Wavelets, CRC Press
Mervan Pašić (2005.), Wavelet, integralne i diskretne transformacije (skripta), FER, Zagreb

General

ID 154914
  Winter semester
6 ECTS
L0 English Level