Spectral property of certain fractal measures

Let {0,aj,bj}={0,1,2}(mod3) be a sequence of digit sets in Z, and let {Nj=3rj} be a sequence of integers bigger than 1. We call {fj,d(x)=Nj−1(x+d):d∈{0,aj,bj}}j=0∞ a Moran iterated function system, which is a generalization of an IFS. We prove that the associated Moran measure is spectral.