Why its is important the connection between wavelets and filter banks?

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Eduardo Trutié-Carrero

The filter banks do not correspond to Wavelet functions but to the Wavelet decomposition tree that, through the use of the frame Wavelet, provides a wavelet filter bank stable with multiple resolution.

Damian Valdés Santiago

Yes. The are wavelet functions that are defined in the continuous axis like Gaussian wavelet, and there are others, like Daubechies', that don't have analytical expressions.