Orthogonal wavelet

An orthogonal wavelet is a wavelet whose associated wavelet transform is orthogonal. That is, the inverse wavelet transform is the adjoint of the wavelet transform. If this condition is weakened one may end up with biorthogonal wavelets.

The scaling function is a refinable function. That is, it is a fractal functional equation, called the refinement equation (twin-scale relation or dilation equation):

where the sequence ${\displaystyle (a_{0},\dots ,a_{N-1})}$ of real numbers is called a scaling sequence or scaling mask. The wavelet proper is obtained by a similar linear combination,

where the sequence ${\displaystyle (b_{0},\dots ,b_{M-1})}$ of real numbers is called a wavelet sequence or wavelet mask.

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