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10Fall_hw11soln - ECE210 Fall 2010 Homework 11 Solution 1...

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Unformatted text preview: ECE210 - Fall 2010 - Homework 11 Solution 1. Problem 9.1 (a) in text. Solution: 1 2. Problem 9.4 in text. Solution: 3. Problem 9.7 (a), (e), (f), (g), and (h). Solution: 2 . 4. Problem 9.8 (a) in text. Solution: 3 5. A system has the frequency response H ( ω ) = 1 3+ jω . (a) Find the output y ( t ) for the input f ( t ) = δ ( t ) . (b) Find the output for the input f ( t ) = 2 δ ( t- 1) . (c) Find the output for the input f ( t ) = u ( t- 1) . Solution (a) Method 1(getting the impulse response of the system and do the convolution in time domain). Method 2 (do the convolution in the frequency domain) i. Method 1 Using item 1 in Table 7.2 to take the inverse FT of H ( ω ) : h ( t ) = F- 1 { H ( ω ) } = e- 3 t u ( t ) Note: h ( t ) is the impulse response of the system. Then y ( t ) = f ( t ) * h ( t ) = δ ( t ) * e- 3 t u ( t ) . Using the convolution property of the impuse, see item 1 in Table 9.3 (p.303): y ( t ) = e- 3 t u ( t ) ii. Method 2: Using item 14 in Table 7.2 (p. 229) (F.T. of a delta function): Y ( ω ) = H ( ω ) · F ( ω ) =...
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10Fall_hw11soln - ECE210 Fall 2010 Homework 11 Solution 1...

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