The signal vectors s1 and s2 are used to represent binary symbols 1 and 0, respectively, in

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The signal vectors s1 and s2 are used to represent binary symbols 1 and 0, respectively, in a coherent binary FSK system. The receiver decides in favor of symbol 1 when XTS1 > xTs2 where xTsi is the inner product of the observation vector x and the signal vector si, where i = 1, 2. Show that this decision rule is equivalent to the condition x1 > x2, where x1 and x2 are the elements of the observation vector z. Assume that the signal vectors s1 and s2 have equal energy.

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