Equalization - Digital Communication: Principles and System Modelling - page 104

Unequalized output

τ τ τ τ τ

c − N c − N +1 c 0 c N −1 c N

Tap gain
adjustment
algorithm

Equalized output

Fig. 5.10 Linear transversal filter

N

g E ( t ) = c n δ ( t − n τ ) (5.22)

n =− N

and the corresponding frequency response is

N

c n e j 2 π fn τ G E ( f ) = (5.23)

n =− N

Since, P ( f ) G T ( f ) H ( f ) G R ( f ), and p(t) is the inverse Fourier transform of P(f),

the equalized output signal pulse

=

N

q ( t ) = c n p ( t − n τ ) (5.24)

n =− N

Applying the zero forcing condition at t = mT B ,

N

q ( mT B ) = c n p ( mT B − n τ ) ; m = 0, ± 1, ± 2, ... ± N (5.25)

n =− N

Since, there are 2N+1 equalizing coefficient, we can control only 2N+1 sampled
values of q(t). Specially,

1, m

N

= 0

q ( mT B ) = c n p ( mT B − n τ ) = (5.26)

0, m =± 1, ± 2, ... ± N

n =− N