b. Determine the minimax threshold.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:21. Consider a binary communication system. The rectangular pulse p(t) and the triangular
pulse q(t) are defined by
p(t) =
s1, 0 <t<T,
else,
and
-→, 0st<T,
q(t) =
else.
To send "1", p(t) is transmitted. To send "0", –q(t) is transmitted. The channel is
contaminated by AWGN with power spectral density of No/2. The following receiver is
used for detection.
T
h(t)
> y or < y
The impulse response of the LTI filter h(t) is given by

Transcribed Image Text:(1, 0 <t < 2T/3,
h(t) = {",
else.
a. Suppose that “l" is sent. Determine the probability of error in terms of T,y,No.
b. Determine the minimax threshold.
c. Suppose that you can change the LTI filter and the threshold at the receiver.
i. Sketch the impulse response of the optimal filter.
ii. Determine the probability of error with the optimal filter and the
associated optimal threshold.
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