I run the haar transform for [9,7,3,5] (using wavelets package) and I'm not figuring out how to achieve the output coefficients. I believe that the unnormalized result would be: [6,2,1,-1]. From what I've read, the normalization is done by multiplying each coefficient by 2^(-j/2), but this shouldn't be the case.
library(wavelets)
wt <- dwt(c(9,7,3,5), filter="haar", boundary="periodic", fast=FALSE)
wt
 
    