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mid-term1

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

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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

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1. (10 points) Find the Fourier transform of x ( t ) = 5Λ parenleftbigg t + 1 2 parenrightbigg . Solution: X ( f ) = 5 × 2sinc 2 (2 f ) e j 2 πf 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: Λ( t ) sinc 2 ( f ) Using duality: sinc 2 ( t ) Λ( - f ) = Λ( 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 π t y ( t ) Solution: H ( f ) = 1 1 + j 2 πf y ( t ) = H (5) x ( t ) = 1 1 + j 10 π e j 10 πt 4. The two-sided power spectral density of a white noise is equal to 1 μ 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 μW/kHz = 2 × 10 MHz × 1 mW/MHz = 20 mW (b) 10 × 1 = 10 mW 2
5. (15 points) Find the signal x ( t ) whose Fourier transform is X ( f ) = 1 + cos ( πfT ) 2 Π parenleftbigg fT 2 parenrightbigg .
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mid-term1 - ECE 5520 Spring 2011 Mid Term 1 Feb 1 2011 Time...

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