Problem 3. Suppose we receive a BPSK signal of the form r(t) = A₁ cos(2π fet) +n(t), 0≤t≤T = where n(t) is a noise process, T = 1 sec, fc = 1 KHz and A₁ ±2 with equal probability. The signal is demodulated in an optimal manner and then an optimal threshold is used in making a decision. For demodulation assume the received signal r(t) is mixed with a cosine wave of amplitude 1 with the same frequency and phase of the transmitted signal of interest and then low pass filtered by integrating from 0 to T. With this approach suppose at the output of the demodulator (just prior to the threshold comparator) the noise (call it n) is characterized by the density 1 1 += -2.0 ≤ n < 0 2 p(n) = 1 1 = 2 4 -n, 0

Problem 3. Suppose we receive a BPSK signal of the form r(t) = A₁ cos(2π fet) +n(t), 0≤t≤T = where n(t) is a noise process, T = 1 sec, fc = 1 KHz and A₁ ±2 with equal probability. The signal is demodulated in an optimal manner and then an optimal threshold is used in making a decision. For demodulation assume the received signal r(t) is mixed with a cosine wave of amplitude 1 with the same frequency and phase of the transmitted signal of interest and then low pass filtered by integrating from 0 to T. With this approach suppose at the output of the demodulator (just prior to the threshold comparator) the noise (call it n) is characterized by the density 1 1 += -2.0 ≤ n < 0 2 p(n) = 1 1 = 2 4 -n, 0

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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