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Examples with the use of matched filters.

The theory and rationale behind matched filter receivers can be found in Matched Filters .

s 1 t t for 0 t T

s 2 t t for 0 t T

h 1 t T t for 0 t T

h 2 t T t for 0 t T

t 0 t 2 T s 1 t s 1 h 1 t
s 1 t 0 t T t 0 t 1 2 T t 2 0 t 1 3 3 t 2 2 T t 3
s 1 T T 3 3

Compared to the correlator-type demodulation

1 t s 1 t E s
s 11 0 T s 1 1
0 t s 1 1 1 E s 0 t 1 E s 1 3 t 3

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Assume binary data is transmitted at the rate of 1 T Hertz.

0 b 1 s 1 t s t for 0 t T

1 b -1 s 2 t s t for 0 t T

X t i P P b i s t i T

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Source:  OpenStax, Digital communication systems. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10134/1.3
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