Fourier decay rate of coin-tossing type measures

The Fourier decay rate of a coin-tossing type measure is investigated. Explicit estimation is given. Our method relies upon a classical result of Hartman and Kershner. As an application, we present a new example of a measure whose Fourier decay rate could be as slowly as we please, and for this measure almost every point is absolutely normal.
Comment: 16 pages