# HW10 - j ) = . 5 1 + j-. 5 3 + j , (1) and use p. 290,...

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ECE 301, Homework #10, due date: 11/3/2010 http://cobweb.ecn.purdue.edu/ chihw/10ECE301F/10ECE301F.html Question 1: [Basic] p. 334, Problem 4.4. Question 2: [Basic] p. 336, Problem 4.10. Question 3: [Basic] p. 336, Problem 4.12(a). Question 4: [Basic] p. 336, Problem 4.13. Question 5: [Basic] 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 6: [Advanced] p. 337, Problem 4.18. Question 7: [Basic] p. 341, Problem 4.26(a). Question 8: [Advanced] p. 341, Problem 4.32(a,b). Question 9: [Advanced] p. 341, Problem 4.32(c,d). Question 10: [Advanced] p. 345, Problem 4.33(a). (Hint: You might need to derive something similar to the following equality.) 1 3 + 4 - ω 2 = 0 . 5((3 + ) - (1 + )) (1 + )(3 +

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Unformatted text preview: 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 11: [Basic] p. 346, Problem 4.35(b). No need to do the sketch. Question 12: [Basic] p. 346, Problem 4.36(a). [Optional] If you are interested, nd the impulse response (b). In reality, people have diculty generating a real impulse signal as an input to a LTI system since a real impulse requires innitely large amplitude. As a result, they try to use a dierent input instead. 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....
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## This note was uploaded on 02/07/2011 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue University-West Lafayette.

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HW10 - j ) = . 5 1 + j-. 5 3 + j , (1) and use p. 290,...

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