Construction of a class of spectral measures

Let the iterated function systems {Si}(i=1) (N) be defined by S-i(x) = (-1) (i-1)rho(x + di), x is an element of R, di is an element of D, where 0 <rho< 1, and D is a finite subset of Z. Let the measure mu(rho),P be generated by the IFS and the probability weight P = {pi}(i =1)(N). In this paper, we introduce a new way to consider the spectrality of mu(rho), P, and obtain a sufficient and necessary condition for N = 2, and construct two examples of spectral measures for N = 2L >= 4 and N = 2L + 1, respectively.