a尺度紧支撑Riesz小波的构造

Construction of Riesz Wavelets of Dilation Factor a with Short Support

从由m阶B样条函数Bm(m∈N)生成的多分辨分析出发,给出一种构造具有a尺度、最短支撑、m阶消失矩、m-12阶正则性的Riesz小波的过程,并且系统X(ψ)构成L2(R)的Riesz基,数值算例支持了本文提出的小波构造方法.

From the muhiresolution analysis generated by the B-spline of order m,this paper is to construct the shortest supported Riesz wavelet of dilation factor a with m vanishing momenls and m-1/2regularity. Further,the system X（Ф） forms a Riesz basis for L2（R）.Finally, a numerical example is given.