Dyadic dilation

For efficient calculations dyadic dilations d = 2 ) of an integer dilation level j (usually called a resolution level) and dyadic translations (t = kd) with an integer translation level k are used. Rearranging Equation 4.62 yields... 

Wavelets form a tool for constructing stable bases of W = L (M). The basis Wj of the space Vj is constructed by means of dyadic dilations and translations of a single scaling function ... 

Usually, the dilation parameter 5 is discretized along the dyadic sequence,... 

The discretization of the dilation parameter need not be dyadic. Discretization schemes with integer or noninteger factors are possible and have been suggested. The reconstruction of Fit) is given by... 

As a result of the dyadic discretization in dilation and translation, the members of the wavelet family are given by... 

---