Page 187 - Fiber Optic Communications Fund

168 Fiber Optic Communications

Duobinary pulse
1
~
p( f )
x (t)
in
Impulse –T b 0 2T b
+ H ( f )
N
x out (t) = p(t)
Delay
T b
Delay-and-add filter

Figure 4.33 Duobinary pulse generation.

as shown in Fig. 4.33. Using Eq. (4.96), Eq. (4.95) can be written as
1
̃ p(f)= [1 + exp (i2fT )]H (f). (4.97)
b
N
B
If an impulse is applied to the filter with the transfer function ̃p(f), the output is a duobinary pulse p(t) (see
Fig. 4.33). This is because the output x (t) and input x (t) of Fig. 4.33 are related by
out
in
̃ x (f)= ̃x (f)̃p(f). (4.98)
out in
For an impulse, ̃x (f)= 1. Therefore, we have
in
x (t)= p(t). (4.99)
out
Fig. 4.34 shows the duobinary encoding scheme using the pulse shown in Fig. 4.33. The impulse generator
generates a positive impulse if the input is +1 V and it generates a negative impulse if the input is −1 V.
The delay-and-add filter in conjunction with a Nyquist filter generates the corresponding duobinary pulses.
Optical generation of partial response formats based on duobinary pulses is discussed in Ref. [8]. Fig. 4.35
shows the schematic of optical duobinary generation. The duobinary encoder shown in Fig. 4.35 could be
realized using either a delay-and-add filter (Fig. 4.26) or a delay-and-add filter in conjunction with a Nyquist

Delay-and-add filter
Differentially encoded
NRZ data Impulse
b(t) generator y(t) Duobinary data
+ H N ( f)
h(t) m(t)
Delay
T b

Figure 4.34 Duobinary encoder.