Four-Channel Tight Wavelet Frames Design Using Bernstein Polynomial

The paper provides a novel technique for designing tight frame wavelet filters through the use of Bernstein polynomials. The perfect-reconstruction conditions of tight wavelet frame filters are established by using parameters of the Bernstein polynomials. The desired number of vanishing moments can be easily achieved by setting the appropriate parameters of the Bernstein polynomial to zero. The filters are obtained by the spectral factorization method and constructed by the appropriate parameters. The design technique is flexible in that it allows low-pass filters and high-pass filters with different characteristics to be designed easily.