Let k denote the differentially encoded phase in the /4-shifted DQPSK. The symbol pairs (I, Q) generated by this scheme may be defined as where

Let ∆θk denote the differentially encoded phase in the π/4-shifted DQPSK. The symbol pairs (I, Q) generated by this scheme may be defined as where Ik and Qk are the in-phase and quadrature components corresponding to the kth symbol show that this pair of relations can be expressed simply as Ik = cos θk Qk = sin θk where θk is the absolute phase angle for the kth symbol.