# HW9 - For example, with the input being x ( t ) as...

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ECE 301, Homework #9, due date: 3/31/2010 http://cobweb.ecn.purdue.edu/ chihw/10ECE301S/10ECE301S.html Question 1: [Basic] p. 334, Problem 4.3. Question 2: [Basic] p. 334, Problem 4.4. Question 3: [Basic] p. 336, Problem 4.10. Question 4: p. 336, Problem 4.12(a). Question 5: p. 336, Problem 4.13. Question 6: p. 337, Problem 4.18. Question 7: For a LTI system with the impulse response h ( t ) = sin(2 t ) πt . Find the frequency response H ( ). This LTI system is an ideal low-pass ﬁlter. What is the cutoﬀ frequency. If the input x ( t ) = cos( t ) + sin(3 t ), ﬁnd the output y ( t ) = h ( t ) * x ( t ). Question 8: p. 346, Problem 4.36(a). [Optional] If you are interested, ﬁnd the impulse response (b). In reality, people have diﬃculty generating a real “impulse” signal as an input to a LTI system since a real “impulse” requires inﬁnitely large amplitude. So they try to use a diﬀerent input instead.

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Unformatted text preview: For example, with the input being x ( t ) as described in Problem 4.36, they then record the output y ( t ). This question shows how to derive the impulse response h ( t ) from x ( t ) and y ( t ) when we cannot directly generate an impulse input. Question 9: p. 345, Problem 4.33(a). (Hint: You might need to derive something similar to the following equality.) 1 3 + 4 j- 2 = . 5((3 + j )-(1 + j )) (1 + j )(3 + j ) = . 5 1 + j-. 5 3 + j , (1) and use p. 290, Example 4.1. Let x ( t ) = e-3 t U ( t ). Find out the response of this LTI system. Question 10: p. 346, Problem 4.35(b). No need to do the sketch....
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## HW9 - For example, with the input being x ( t ) as...

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