563489578934

468
Random Processes and Spectral Analysis Chap. 6
s(t)
1
T
(a) Input Signal
t 1 t 2
s (–t)
t
1
–t 2 –t 1
t
(b) “Backwards” Signal
h(t)=s(t 0 -t),
1.0
(c) Matched-Filter Impulse Response
where t 0 =t 2
t 0 +T
t 0 =t 2
T
t
s 0 (t)
T
0.75T
0.5T
0.25T
t 2 t 0
t
(d) Signal Out of Matched Filter
Figure 6–16 Waveforms associated with the matched filter of Example 6–14.
2T
We will use t 0 = t 2 because this is the smallest allowed value that satisfies the causal condition
and we would like to minimize the time that we have to wait before the maximum signal level
occurs at the filter output (i.e., t = t 0 ). A sketch of h(t) for t 0 = t 2 is shown in Fig. 6–16c. The
resulting output signal is shown in Fig. 6–16d. Note that the peak output signal level does indeed