One way of interpreting Schwarz's inequality for complex integrals is to use the familiar vector inequality: |a + b| 3 |a| + |b|. Equality is satisfied if a = Kb, or if a and b are collinear. In the case of complex functions, it can be shown that equality is satisfied if
(See, for example, Schwartz, 1959, for a detailed proof of Schwarz's inequality.) To apply Equation 7.2-9 to the SMF problem, we note that X(ju) = S(ju) exp(juxo) and Y(ju) = Hm(ju). Thus, the ratio, (n/2) |g(xo)|2/(E No) must be 3 1, and
IJ™S(ju)Hm(ju)exp(jux)du < Jf°|Hm(jufdfJ""|s(jufdu
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