B样条正交小波的构造

The construction of B-spline orthonormal wavelet

基于 Mallat多尺度分析理论 ,用 Daubechies的正交小波构造方法 ,构造出任意阶基数 B样条规范小波 ,并给出了相应的小波函数 ψ、尺度函数 φ、正交镜象滤波器 H和 G的时频响应表达式 .这类小波产生的小波基适用于一维和二维信号分解与重建过程中的 Mallat快速算法 .

Based on Mallats theory of multiscale analysis, we construct the arbitrary order cardinal B spline orthogonal wavelet by using Daubechies method of orthogonal wavelet construction, and derive the general expressions for the corresponding wavelet function ψ ,the scaling function φ , the quadrangular mirror filters H and G both in spectral and spatial domains. The families of the wavelet bases generated by the arbitrary order cardinal B spline orthonormal wavelets are also suitable for Mallats wavelet decomposition and reconstruction algorithms of 1 D and 2 D signals.