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 $\begin{bmatrix}0.1&0.5&0.8&0.5&0.1\end{bmatrix}$ 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 ??
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