Orthonormierte Wavelets mit kompaktem Träger

φ ∈ L2, supp(φ) kompakt

\(\phi (t) \equiv \sqrt 2 \sum\limits_k {{h_k}\phi } (2t - k)\quad bzw.\quad \widehat \phi \left( \xi \right) = H\left( {\frac{\xi }{2}} \right)\widehat \phi \left( {\frac{\xi }{2}} \right),\)

\(\int \phi (t)dt = 1\quad bzw.\quad \widehat \phi \left( 0 \right) = \frac{1}{{\sqrt {2\pi } }},\)

\(\int \phi (t)\overline {\phi \left( {t - k} \right)} dt = {\delta _{0k}}\quad bzw.\quad {\sum\limits_k {\left| {\widehat \phi \left( {\xi + 2\pi l} \right)} \right|} ^2} \equiv \frac{1}{{\sqrt {2\pi } }}.\)