21. Consider a binary communication system. The rectangular pulse p(t) and the triangularpulse q(t) are defined byp(t) =s1, 0 y or < yThe impulse response of the LTI filter h(t) is given by (1, 0

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Answered: b. Determine the minimax threshold.

Math

Advanced Math

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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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

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

(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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