7.2 DUOBINARY WAVEFORMS: SPECTRAL RESHAPING AND ENCODING

First, we discuss the duobinary technique. Consider a binary input train consisting of 1 s and 0 s represented by impulses + ?(t) or ? ?(t), as shown at A in Fig. 7.1. For each ?(t) input at A _, the output at B is [ ?(t)+ ?(t ?T)] with the appropriate sign. We define the impulse response of H ₁ (f) as h ₁ (t):

where is the Fourier transform, and h ₁ (t) the impulse response. Also,

• =speed in b\s

• T=bit interval in seconds

Fig. 7.1: Block diagram of duobinary system.

Since , then

To limit the bandwidth, we place the Nyquist rectangular filter H ₂ (f) after H ₁ (f), as shown in Figure 7.1, and specify H ₂ (f) by the following equation: H ₂ (f)= T for f ?1/2 T and zero elsewhere. The overall transfer function from A to C in Fig. 7.1 represents the duobinary conversion filter H(f) and is given by:

and zero elsewhere.

The impulse response of H(f) is obtained from equation (7.2), and is

Hence, for every input impulse ?(t) at A, the output at C is h(t), with an appropriate polarity. Since the bit interval is T seconds, there will be overlap or ISI between the digits over...