Consider the problem of transmitting information over a channel that
is bandlimited. Further consider the passband
of the channel to be around zero. The channel is best modeled as
The received signal is given by
r
t
=∫-∞∞
X
τ
gt-τdτ+
N
t
=
Y
t
+
N
t
r
t
τ
X
τ
g
t
τ
N
t
Y
t
N
t
(1)
As a consequence of the bandlimited nature of the channel,
Y
t
Y
t
is no longer a time limited signal. As a result, each symbol period is
larger than
TT
and the signal from one symbol period interferes with symbols in
other time periods. This aliasing of signals is refered to as
intersymbol interference (ISI).