Consider a binary communication system. The pulse p(t) and the pulse q(t) are defined by ´A6 + 1, а, + аg, 0sts1, 1 y or < y The impulse response of the LTI filter h(t) is given by Osts1, else. h(t) = {o, Sketch the signals p(t) and q(t). Suppose that "I" is sent. Determine, in terms of No, the probability of а. b. error if y = ag – 2. c. Suppose that you can change the LTI filter and the threshold at the receiver. i. Sketch the impulse response of the optimal filter. Determine the minimax threshold with the optimal filter. Determine the probability of error with the optimal filter and the ii. ii. minimay throehold
Consider a binary communication system. The pulse p(t) and the pulse q(t) are defined by ´A6 + 1, а, + аg, 0sts1, 1 y or < y The impulse response of the LTI filter h(t) is given by Osts1, else. h(t) = {o, Sketch the signals p(t) and q(t). Suppose that "I" is sent. Determine, in terms of No, the probability of а. b. error if y = ag – 2. c. Suppose that you can change the LTI filter and the threshold at the receiver. i. Sketch the impulse response of the optimal filter. Determine the minimax threshold with the optimal filter. Determine the probability of error with the optimal filter and the ii. ii. minimay throehold
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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Suppose a6=6, a7=7, a8 = 8, a9 = 9
Transcribed Image Text:Consider a binary communication system. The pulse p(t) and the pulse q(t) are defined
by
0 st<1,
1<t< 2,
2 <t< 3,
else,
´a6 + 1,
az + ag,
p(t) =
ag,
0,
and
0st<1,
1<t< 2,
2 <t < 3,
else.
ag – 5,
-а, — 2,
0,
To send "l", p(t) is transmitted. To send “0", q(t) is transmitted. The channel is
contaminated by AWGN with two-sided power spectral density of No/2. The following
receiver is used for detection. The receiver decides "I" if the output of the sampler is
q(t) =
bigger than y, and “0" otherwise.
@T, = 2
h(t)
> y or < y
The impulse response of the LTI filter h(t) is given by
0sts1,
else.
Sketch the signals p(t) and q(t).
s1,
h(t) = {
а.
b.
Suppose that “1" is sent. Determine, in terms of No, the probability of
error if y = ag – 2.
c. Suppose that you can change the LTI filter and the threshold at the receiver.
Sketch the impulse response of the optimal filter.
Determine the minimax threshold with the optimal filter.
Determine the probability of error with the optimal filter and the
i.
ii.
iii.
associated minimax threshold.
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