mid-term1 - ECE 5520, Spring 2011 Mid Term 1 Feb. 1, 2011...

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Unformatted text preview: ECE 5520, Spring 2011 Mid Term 1 Feb. 1, 2011 Time: 75 minutes Name: Question Points 1 2 3 4 5 6 7 8 Total 1 1. (10 points) Find the Fourier transform of x ( t ) = 5 parenleftbigg t + 1 2 parenrightbigg . Solution: X ( f ) = 5 2sinc 2 (2 f ) e j 2 f 2. (10 points) Starting from line 15 of Table 2.1, and using the duality property, prove line 16 of Table 2.1. Solution: Line 15: ( t ) sinc 2 ( f ) Using duality: sinc 2 ( t ) (- f ) = ( f ) This is line 16. 3. (10 points) In the system shown below, find the output y ( t ). h ( t ) = e- t u ( t ) x ( t ) = e j 10 t y ( t ) Solution: H ( f ) = 1 1 + j 2 f y ( t ) = H (5) x ( t ) = 1 1 + j 10 e j 10 t 4. The two-sided power spectral density of a white noise is equal to 1 W/kHz. Find its power within (a) (10 points) a passband expanding from 10 MHz to 20 MHz. (b) (10 points) a baseband from- 5 MHz to +5 MHz. Solution: (a) 2 10 MHz 1 W/kHz = 2 10 MHz 1 mW/MHz = 20 mW (b) 10 1 = 10 mW 2 5. (15 points) Find the signal5....
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This note was uploaded on 03/18/2011 for the course ECE 5520 taught by Professor Shamir,g during the Spring '08 term at University of Utah.

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mid-term1 - ECE 5520, Spring 2011 Mid Term 1 Feb. 1, 2011...

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