A new method of estimating wavelet with desired features from a given signal

This paper proposes a new method of estimating both biorthogonal compactly supported as well as semi-orthogonal infinitely/compactly supported wavelet from a given signal. The method is based on maximizing projection of the given signal onto successive scaling subspace. This results in minimization of energy of signal in the wavelet subspace. The idea used to estimate analysis wavelet filter is similar to a sharpening filter used in image enhancement. First, a new method is proposed that helps in the design of 2-band FIR biorthogonal perfect reconstruction filter bank from a given signal. This leads to the design of biorthogonal compactly supported wavelet. It is also shown that a wavelet with desired support as well as desired number of vanishing moments can be designed with the proposed method. Next, a method is proposed to design semi-orthogonal wavelets that are usually infinitely supported wavelets. Here, corresponding to FIR analysis filters, the resulting synthesis filters are IIR filters that satisfy the property of perfect reconstruction.