Equalization - Digital Communication: Principles and System Modelling - page 94

delayed by the system. Due to this, the pulse appearing at the output is dispersed
over an interval which is longer than T B (Fig. 5.2 ).
Due to this dispersion, the symbol of the ith instant is co-occurred with the
delayed and advanced pulses. This will result in Inter-Symbol Interference.

Transmission
System

T B >T B

Dispersed pulse Properly shaped pulse

Fig. 5.2 Cause of Inter-Symbol Interference

5.2 Nyquist Criterion for Distortion Less
Transmission (Zero ISI)

From the discussion of previous section, it can be inferred that, in absence of ISI,
the ith recovered sample at the output should be

y ( t i ) = μ a i

To achieve this sample accurately, the transmitting and receiving filters need to
be designed properly. The transfer function of the entire transmission system, P(f)
needs to be obtained.
The decoding at the receiver end should be such that, the contribution of
the weighted pulse i.e.,

∞

a k p ( iT B − kT B ) at i = kbefreefromISI.Thesaid

k =−∞

condition can be mathematically modeled as

1

for i = k

p ( i − k ) T B = (5.4)

0 for i = k

where, p (0) 1 due to normalization.

If the received pulse satisfies the Eq. ( 5.4 ), then the receiver output given by Eq.
( 5.3 ) reduces to

=

y ( t i ) = μ a i (5.5)

This indicates zero ISI in the absence of noise.