Improved Technique for the Construction of Parametric M-Band Wavelets

Demanding applications of wavelets in OFDM modulation, watermarking, cognitive radio and wireless networks has created an immense interest amongst the researchers to work on the design of good wavelet system. Parametric and M-band wavelets draw a special attention in this category. A commensurate procedure for constructing a superior M-band parametric wavelet system is proposed in this paper. The idea of modulation matrix decomposition and the relation with corresponding polyphase matrix and its factorization is exploited to possible extent to make the design process plain and easy. The appropriate polynomial matrix is put in place to extend the filter design to any required length. The simple property of the Kroneckor product of two matrices is contemplated to achieve M-band design. This paper ponders on the above-mentioned factors and accomplishes the task of designing an M-band parametric wavelet, which is complete in itself. Few examples are used to substantiate the proposed method.