Solution to the orthogonal M-channel bandlimited wavelet construction proposition

While bandlimited wavelets and associated IIR filters have shown serious potential in areas of pattern recognition and communications, the dyadic Meyer wavelet is the only known approach to construct bandlimited orthogonal decomposition. The sinc scaling function and wavelet are a special case of the Meyer. Previous works have proposed a M-Band extension of the Meyer wavelet without solving the problem. One key contribution of this paper is the derivation of the correct bandlimits for the scaling function and wavelets to guarantee an orthogonal basis. In addition, the actual construction of the wavelets based upon these bandlimits is developed. A composite wavelet is derived based on the M scale relationships from which we extract the wavelet functions. The proper solution to this task is proposed which generates associated filters with the knowledge of the scaling function and the constraints for M-band orthogonality.