Show that, for s to be proper complex, its in-phase and quadrature components must be uncorrelated and have the same variance. Let s conform to a ternary constellation defined by s0 = −1, s1 = 0, and...

Show that, for s to be proper complex, its in-phase and quadrature components must be uncorrelated and have the same variance. Let s conform to a ternary constellation defined by s0 = −1, s1 = 0, and s2 = 1. Is this signal proper complex? Is it circularly symmetric? Let x be a discrete random variable and let y = g(x) with g(·) an arbitrary function. Is H(y) larger or smaller than H(x)?