Show that Equation (385a) holds. Hints: start with the expression for Υk(f 0 ) in Equation (384a), use interchange the order of the integrals and the summation such that the innermost integral equals...

Show that Equation (385a) holds. Hints: start with the expression for Υk(f 0 ) in Equation (384a), use interchange the order of the integrals and the summation such that the innermost integral equals the integral on the right-hand side of Equation (384b), and then use the complex conjugate of Equation (383d) (recall that the DPSWF Uk(·) is a real-valued function). Finally, use the fact that both dZ(·) and Uk(·) are periodic functions with a period of unity.