基于复子波的多子波构造

The multiwavelet construction via complex wavelet

在实子波分析中,子波函数缺乏对称性,这样大大限制了实子波的应用领域.复子波具有良好的对称性,但对于实信号进行子波分析时,运算过于复杂,且虚部需要截断.文中从复子波出发,分离其虚部与实部构造出新的多子波.构造出的多子波同时具备紧支性、正交性和对称性.同时免预/后滤波,且相应的滤波器系数对称,使得运算复杂度降低.

For lack of symmetry in real wavelet analysis, its application is limited. Complex wavlet has good symmetry, but it is too complicated to analyze the real signal and the imaginary part of the processed result is truncated. This paper separates the real part and the imaginary part from the complex wavelet to construct the multiwavelet with good properties, such as short support, orthogonality and symmetry. The multiwavelet via this method does not any pro/post filter, and its symmetry of filter coefficients reduces the computation complication.