That is, the local squared peak signal-to-noise ratio at x = xo is maximum. In other words, the SMF acts to give a maximum output when a particular s(x) for that Hm(ju) is present. The SMF system does not try to recover and reproduce the image, s(x), but only detects its presence by examining p(xo) for a maximum. The input signal, s(x), must have finite "energy." By Parseval's theorem,

E = J s2 (x)dx = J |s(ju)2du = J S * (ju)S(ju)du 7.2-6

To find the desired SMF weighting function or transfer function, examine the conditions whereby the ratio below is maximized:

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