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Col Univ SPRING 2005 ELEN 4815 MIDTERM FINAL VERSION-2005

# Col Univ SPRING 2005 ELEN 4815 MIDTERM FINAL VERSION-2005 -...

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1 Random Signals and Noise ELEN E4815 Columbia University Spring Semester- 2005 Prof I. Kalet 9 March 2005 Midterm Examination Length of Examination- 1:45 hours Answer All questions Good Luck!!!

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2 Problem #1 (34 Points) The autocorrelation function, R x ( τ ), of a random process, x(t), is shown below. R x ( τ ) A A/2 -T 0 T τ a) What is the total power in this random process? b) Is there a d-c component in this random process? Explain your answer. c) If your answer to part (b) was positive, how much power is there in the d-c component of the random process, x(t)? d) Find and draw the power spectral density of this random process.
3 e) Now suppose that the power spectral density of a WSS random process, x(t), is given below. P x (f) A A/2 -W 0 W f What is the total power in this random process? f) Is there a d-c component in this random process? Explain your answer.

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4 Problem #2 (33 points) Consider the random process, x(t), the so-called random telegraph signal (shown below). In this signal, which started at -
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Col Univ SPRING 2005 ELEN 4815 MIDTERM FINAL VERSION-2005 -...

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