Wavelet function, scaling function and discrete wavelet transform

In this paper, we discuss the general condition for a function to be a wavelet function or a scaling function. We also discuss the condition for the functions to form a multiresolution wavelet decomposition and reconstruction. The relationships between continuous wavelet transform and discrete wavelet transform are established.<<ETX>>

[1]  Stéphane Mallat,et al.  Multifrequency channel decompositions of images and wavelet models , 1989, IEEE Trans. Acoust. Speech Signal Process..

[2]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[3]  Zhi-Quan Luo,et al.  Design of an optimum wavelet for cancellation of long echoes in telephony , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[4]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..