Title :
Mutual transformations between Haar wavelet and arithmetic spectra
Author :
Falkowski, Bogdan J.
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
Abstract :
The mutual conversions between Haar wavelets and arithmetic functions and spectra in the form of matrix decomposition corresponding to fast transforms and as layered vertical and horizontal Kronecker matrices are introduced. The new relations apply to an arbitrary dimension of the transform matrices and allow direct conversions to be performed between arithmetic and Haar wavelet functions and their corresponding spectra.
Keywords :
Haar transforms; matrix decomposition; spectral analysis; wavelet transforms; Haar wavelets; arbitrary dimension; arithmetic functions; arithmetic spectra; fast transforms; horizontal Kronecker matrices; matrix decomposition; mutual transformations; transform matrices; vertical Kronecker matrices; Arithmetic; Artificial intelligence; Boolean functions; Digital signal processing; Discrete transforms; Discrete wavelet transforms; Logic functions; Matrix decomposition; Spectral analysis; Wavelet transforms;
Conference_Titel :
Circuits and Systems, 2002. ISCAS 2002. IEEE International Symposium on
Print_ISBN :
0-7803-7448-7
DOI :
10.1109/ISCAS.2002.1010589
