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COL UNIV SPRING 2006 ELEN E4815 FINAL EXAM MAY 2006

# COL UNIV SPRING 2006 ELEN E4815 FINAL EXAM MAY 2006 - 1...

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1 Columbia University Random Signals and Noise ELEN E4815 Spring Semester- 2006 Prof I. Kalet 10 May 2006 Final Examination Length of Examination- Three hours Answer All Questions GOOD LUCK!!!

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2 Problem #1 The power spectral density, P n (f), of a narrow-band gaussian WSS random process, n(t), is shown below. The process can be represented by the equation below n(t)=n R (t) cos 2 π f 0 t – n Q (t) sin 2 π f 0 t P n (f) A f -12W -8W 0 8W 12W a. What is the total average power in this random process? b. For what value of f 0 , will the power spectral densities of n R (t) and n Q (t) be flat? c. Draw the power spectral densities of n R (t) and n Q (t) for the value of f 0 found in part (b). d. What will be the average powers of n R (t) and n Q (t)? e. Draw the spectral densities for n R (t) and n Q (t), if f 0 =9W. f. What will be the average powers of n R (t) and n Q (t), if f 0 =9W?
3 Problem #2 We showed in class that any narrowband random process, n(t), could be written in the form n(t)=n R (t) cos 2 π f 0 t – n Q (t) sin 2 π f 0 t where n R (t) and n Q (t) were defined in class.

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