hw5_energy_noise

Hw5_energy_noise - Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring 2008 Homework #5: Energy and Noise Issued: March 7, 2008 Due: March 14, 2008 1. Consider the probability density function f X (x) of random variable X shown below in Figure 1. -0.5 0.5 1 x () X f x Figure 1 a) What is the mean of X ? b) What is the variance of X ? c) What is the probability of -0.1 X 0.2 ? 2. Consider the digital receiver and accompanying signals shown below: t t 4 0 in(t) out[n] Sample Slice x f X (x) PDF of Noise at sample t o (at a given sample t o , n(t o ) = X) 0 4 0 n(t) Noise t o 3 -3 6 1 a) Assuming that the probability of sending a 0 symbol is 1/2, the probability of sending a 4 symbol is 1/2, what is the slicing threshold position that results in smallest bit error rate? What is that bit error rate?
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2 b) Given the same conditions as in part (a), what is the Signal-to-Noise Ratio (SNR) at the receiver? Specify the SNR(dB) = 10log10(Z), where Z = var(signal)/var(noise). c)
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This note was uploaded on 08/23/2009 for the course EECS 6.02 taught by Professor Terman during the Spring '08 term at MIT.

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Hw5_energy_noise - Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.02 Intro to EECS II Spring

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