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4) Consider a binary transmission scheme with two waveforms s₁(t) = A{u(t) - 2u(t-1)+2u(t-2)-u(t-3)} and S2(t) = A{u(t)u(t-4)}. The received signal is r(t) = sm(t)+n(t), where m is determined by a single bit of information to be transmitted and n(t) is AWGN with power spectral density No/2 W/Hz. a) Sketch the impulse responses of the matched filters to be used in signal demodulation. b) Sketch the output of the matched filters to the input s₁(t). c) Determine the variance of the noise of the matched filter outputs at t = 3. d) Determine the probability of error as a function of A and No.

4) Consider a binary transmission scheme with two waveforms s₁(t) = A{u(t) - 2u(t-1)+2u(t-2)-u(t-3)} and S2(t) = A{u(t)u(t-4)}. The received signal is r(t) = sm(t)+n(t), where m is determined by a single bit of information to be transmitted and n(t) is AWGN with power spectral density No/2 W/Hz. a) Sketch the impulse responses of the matched filters to be used in signal demodulation. b) Sketch the output of the matched filters to the input s₁(t). c) Determine the variance of the noise of the matched filter outputs at t = 3. d) Determine the probability of error as a function of A and No.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 40E
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4) Consider a binary transmission scheme with two waveforms s₁(t) = A{u(t) - 2u(t-1)+2u(t-2)-u(t-3)} and S2(t) = A{u(t)u(t-4)}. The received signal is r(t) = sm(t)+n(t), where m is determined by a single bit of information to be transmitted and n(t) is AWGN with power spectral density No/2 W/Hz. a) Sketch the impulse responses of the matched filters to be used in signal demodulation. b) Sketch the output of the matched filters to the input s₁(t). c) Determine the variance of the noise of the matched filter outputs at t = 3. d) Determine the probability of error as a function of A and No.
Transcribed Image Text:4) Consider a binary transmission scheme with two waveforms s₁(t) = A{u(t) - 2u(t-1)+2u(t-2)-u(t-3)} and S2(t) = A{u(t)u(t-4)}. The received signal is r(t) = sm(t)+n(t), where m is determined by a single bit of information to be transmitted and n(t) is AWGN with power spectral density No/2 W/Hz. a) Sketch the impulse responses of the matched filters to be used in signal demodulation. b) Sketch the output of the matched filters to the input s₁(t). c) Determine the variance of the noise of the matched filter outputs at t = 3. d) Determine the probability of error as a function of A and No.
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