Complex rational orthogonal wavelet and its application in communications

This letter proposes a generalized method to construct complex wavelets under the framework of rational multiresolution analysis, MRA(M), where M is a rational number. Theorems and examples are given for the construction of complex rational orthogonal wavelets (CROWs) whose real and imaginary parts form an exact Hilbert transform pair. Since the classical Mallat's MRA is a special case of the rational MRA(M) with M=2, the theorems hold for the construction of complex dyadic wavelets. Based on a rational MRA(M) with 1