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376 Fiber Optic Communications

s' (t) s 1 (t) s (t * T b ) s' (t)
1
1
1

0 T b 2T b
0 T b 2T b t t

s' 0 (t) s 1 (t) s' 0 (t)

0 T b 2T b t 0 T b 2T b t

s 0 (t * T b )
set I set II

′
′
Figure 8.23 Orthogonal signals s (t) and s (t) constructed using s (t) and s (t).
1 0 1 0
′
′
′
′
′
s (t), and this is shown in Fig. 8.24. H () and H () are the filters matched to s (t) and s (t), except that
0 1 0 1 0
they can have an arbitrary constant phase shift:
′
′∗
H ()= s ( − ) exp (iT + i), j = 0, 1. (8.302)
j j c b
Taking the Fourier transform of Eq. (8.299) (set I) and using the shifting property of the Fourier transform,
∗
∗
′
H ()=[s ( − )+ s ( − ) exp (iT )] exp (iT + i)
1 1 c 1 c b b
= H ()[1 + exp (iT )], (8.303)
1 b
where H () is the filter matched to s (t)e −i c t except for the phase factor (see Eq. (8.277)). Fig. 8.25 shows
1 1
′
the realization of H () using a delay-and-add filter. The second term of Eq. (8.303) corresponds to the delay
1
by T . Similarly,
b
′
∗
∗
H ()=[s ( − )+ s ( − ) exp (iT )] exp (iT + i)
0 1 c 0 c b b
= H ()[1 − exp (iT )]. (8.304)
b
1