final_221_2008 - comes 1 | a | X ( ω a ). (b) (i) A signal...

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NSU 2008 Fall ETE-221/CEG-383 Finals Sec: 1 Time: 80 mins Marks:30 Answer all of the following: 1. Consider the signals x ( t ) = rect ( t 2 ) and y ( t ) = r ( t ) - r ( t - 1). Calculate x * y ( t ) and R xy ( t ) = i -∞ x ( τ + t ) y ( τ ) . (4+4) 2. (a) Consider periodic functions whose period is 2 π . Find the complex fourier coe±cients of the function x ( t ) = rect ( t 2 ) , - π t π . (b) Using the above coe±cients ²nd the autocorrelation function R xx ( t ) = 1 T i T/ 2 - T/ 2 x * ( t + τ ) x ( τ ) . (4+6) 3. (a) Show that under a scaling t at , the Fourier transform of x(t) be-
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Unformatted text preview: comes 1 | a | X ( ω a ). (b) (i) A signal x ( t ) = Ae-at 2 is fed as the input to a system whose output is given by y ( t ) = x 2 ( t ). What is the Fourier tranform of the output? (ii) If y(t) is applied to a second system which is LTI with the response h ( t ) = Be-bt u ( t ), ²nd the Fourier transform of the output of the second system. (3+4+5) 1...
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