B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

876 APPENDIX B: CAUCHY-SCHWARZ INEQUALITY
with equality only if I Y ( w) I = c IX ( w) I, where c is an arbitrary constant. Now recall that
li b X(w)Y(w) dwl ::: l b IX(w) IIY(w) l dw = l b IX(w)Y(w) l dw
(B.6)
with equality if and only if Y(w) = cX * (w), where c is an arbitrary constant. Equation (B.2)
immediately follows from Eqs. (B.5) and (B.6).