【摘要】 为了能够构造具有良好性质的m带正交小波,本文提出一种利用插值细分法构造紧支正交小波的方法.首先基于2N点m-ary插值细分法构造m带紧支正交的可细化函数,该可细化函数的自相关函数是插值细分法的基极限函数;然后根据可细化函数构造正交小波,并研究了正交小波的消失矩性质.构造算例结果表明,利用文中方法可以构造出新的具有更大自由度的含参m带正交小波,并证明了该方法的实用性.更多还原

【Abstract】 The aim of the paper is to construct an m-band orthonormal wavelet with some good properties.A new method to construct m-band orthonormal wavelets based on m-ary subdivision schemes is presented.First,we construct an m-band orthonormal refinable function based on an m-ary 2N-point interpolatory subdivision scheme,whose basic limit function is the autocorrelation function of the refinable function,and then construct orthonormal wavelets using the orthonormal refinable function.Moreover,the property of vanishing moments of the orthonormal wavelets is analyzed.The feasibility of the method is exposed in three examples and a new 2-band orthonormal wavelet with a tension parameter is constructed.更多还原