Fourier decay for homogeneous self-affine measures

We show that for Lebesgue almost all d-tuples (theta(1), ..., theta(d)), with vertical bar theta(j)vertical bar > 1, any self-affine measure for a homogeneous non-degenerate iterated function system {Ax + a(j)}(j=1)(m) in R-d, where A(-1) is a diagonal matrix with the entries. (theta(1), ..., theta(d)), has power Fourier decay at infinity.