句法

输入参数

输出参数

Algorithms

For compactly supported wavelets defined by filters, in general no closed form analytic formula exists.

The algorithm used is the cascade algorithm. It uses the single-level inverse wavelet transform repeatedly.

Let us begin with the scaling function ϕ.

由于φ还等于φ_0,0，此功能的特征在于正交框架中的以下系数：

This expansion can be viewed as a wavelet decomposition structure. Detail coefficients are all zeros and approximation coefficients are all zeros except one equal to 1.

然后，根据以下结果，我们使用重建算法在Dyadic网格上近似函数φ：

对于表单的任何二次理性X=N2^-J.其中该功能是连续的，在哪里jis sufficiently large, we have pointwise convergence and

哪里C是常数，并且α是正常常数，这取决于小波规律。

然后使用φ对二元结构的良好近似，我们可以在二次间隔中使用分段常数或分段线性插值η，其具有相似的指数率发生均匀的收敛性：

So using aj-step reconstruction scheme, we obtain an approximation that converges exponentially towards ϕ whenj走向无限。

Approximations are computed over a grid of dyadic rationals covering the support of the function to be approximated.

Since a scaled version of the wavelet function ψ can also be expanded on the (ϕ_−1,N））_N，可以使用相同的方案，在单级重建以适当的小波分解结构开始之后。近似系数是所有零，细节系数是除一个等于1之外的所有零。

For biorthogonal wavelets, the same ideas can be applied on each of the two multiresolution schemes in duality.

也可以看看

intwave|WaveInfo.|Wfilters.