Wavelet Filter Coefficients from Scaling Filter Coefficients I am trying to develop a new type of wavelets and I found out a function that following a particular two scale relation. The function at a scale $t$ say $x(t)$ can be related in a finer scale $x(2t)$ by the following relation:

$$x(t)=0.1x\left(2t\right)+ 0.5x\left(2t-1\right)+0.8x\left(2t-2\right)+0.5x\left(2t-3\right)+0.1x\left(2t-4\right),$$ 

This is found out by trial and error method by simply changing the values. Now I know that the points $\begin{bmatrix}0.1&amp;0.5&amp;0.8&amp;0.5&amp;0.1\end{bmatrix}$ can be considered as  the scaling filter coefficients. Now the problem is finding the wavelet filter coefficients, I am not able to find out a particular relation connecting scaling filter coefficients and wavelet filter coefficients. Is there is a relation connecting the two ??
For perfect reconstruction you need:

$$ g \left[ n \right] * \hat{g} \left[ n \right] + h \left[ n \right] * \hat{h} \left[ n \right] = \delta \left[ n \right] $$

Where $ g \left[ n \right] $ is the Analysis Wavelet Function, $ \hat{g} \left[ n \right] $ is the Synthesis Wavelet Function, $ h \left[ n \right] $ Analysis Scaling Function and $ \hat{h} \left[ n \right] $ is the Synthesis Scaling Function.

Practically, Scaling Function is the LPF and Wavelet Function is the HPF.