PROPERTIES OF RANDOM S IGNALS IN WAVELET DOMAIN

I. Int rod uct io n1) The wavelet transform have been used mainly in the fields of signal processing, image coding and compression,and in certain areas of mathematics, as in solution of partial differential equations or numerical analysis[1][2][3][4]. Recently an enormous interest has emerged on the use of wavelet transforms in several areas. One of these areas is to understand the statistical behavior of random signals in wavelet domain. Basseville et al.[5] studied random processes defined on a multiscale grid of wavelet decomposition coefficients but its relationship to conventional notions of stationarity for random processes is unclear. Wornell[6] used wavelet transform to synthesize 1/f processes. His work assumes a very simple correlation structure for the wavelet coefficients are all independent. And also Marsry[7] studied stationary increment processes on the wavelet domain and applied to fractional Brownian motion(fBm) but his work did not consider mismatching between wavelets in L 2 ( R) and ensembles of stationary increment processes in L 1 ( R). Dijkerman[8] used wavelet transform to analyze time domain AR processes but his research was confined that characteristic of time domain AR process representations in wavelet domain and has not tried to an AR modeling i