The Compactly Supported Four-band Complex Wavelets

This paper mainly study the general construction of4-band complex wavelets. The complex wavelet has some irreplaceable advantages in its ap-plication. However, there is the relatively few researches. The construction of M-band complex wavelet is especially complex, and there are few exam-ples of application that can be selected. At the beginning, the construc-tion of compactly supported4-band orthonormal complex wavelets with linear phase are put forward, with the specific examples with the common length of8,12,16. In the complex wavelets, even the lack of linear phase, real and imaginary parts of the filter may have symmetry. For this feature, the author studies another complex wavelets with nonlinear phase, which have symmetric or antisymmetric filter coefficient, although they lose their lin-ear phase,but their regularity is better. In making discrete signal processing, computational complexity of its structure and linear phase case have no es-sential differences, with the length of8,12and16of such complex wavelet equally. This paper studies two structures formed two complex wavelet class, whose construction method has versatility.