Multi-band wavelets are newly emerging branch in wavelet family and could have better properties than dyadic wavelets in
terms of symmetry, orthogonality, compact support and smoothness. The purpose of this paper is to present a new method for
constructing the filter banks of 3-band symmetric bi-orthogonal wavelet using a scaling function of linear spline function. To
construct such 3-band wavelet with desirable properties, a set of linear algebra equations can be listed according to the
requirements of the bi-orthogonal multi-resolution analysis. And these equations are then solved to obtain the filter
coefficients. The properties of the filters and the multi-resolution analysis (MRA) in signal processing are discussed.
Experiments show that the 3-band filter banks could be potentially better in signal processing than dyadic wavelets.
Different type of wavelets has been constructed in order to be adapted for different applications. In this paper, we have got a new family of wavelets through self-correlation function of Daubechies wavelets and discussed their some properties and applications.
Fractal coding of digital images offers many promising qualities. However the coding process suffers from the long search time in the Domain Block Pool. We present a novel idea for speeding up search and improving compressive ratio, based on the hypothesis that those correlative Range Blocks should have a common code. Experimental result on 512 X 512 Lenna image is 32.8 dB at 0.625 b/pixel and 29.76 dB at 0.214 b/pixel.