Why is it important for the scaling function to have unit area in wavelets?
This is just a normalization that makes some formulas simpler. An alternative would be to require that the $L^2$norm (or some other norm) be $1$. 


Why is it important for the scaling function to have unit area in wavelets? 


This is just a normalization that makes some formulas simpler. An alternative would be to require that the $L^2$norm (or some other norm) be $1$. 

