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....  RT  RT  RT 0 0 0 ( )dt Y ( )dt Y ( )dt Y sample at
t=T 3 1 2 3 Y (t) i (t)dtgj3=1 are su cient statistics for optimal detection. Three su cient statistics are needed
i
because there are three basis signals for the signal set. fYi = RT
0 4 b) Yes, the four components do provide su cient information for optimal detection. The basis signals f i (t)gji
were calculated from fsk (t)gji , hence we can nd fYi = Y (t) i (t)g from fY (t) sk (t)g. Since the fYi g are
su cient statistics for optimal detection, it follows that fY (t) sk (t)g is as well.
3
=1 4
=1 5...
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 Spring '09

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