# HW9 - jω = 5 1 jω 5 3 jω(1 and use p 290 Example 4.1 Let...

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ECE 301, Homework #9, due date: 11/02/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE301F/11ECE301F.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: [Basic] p. 336, Problem 4.12(a). Question 5: [Basic] p. 336, Problem 4.13. Question 6: [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 7: [Advanced] p. 337, Problem 4.18. Question 8: [Basic] p. 341, Problem 4.26(a). Question 9: [Advanced] p. 341, Problem 4.32(a,b). Question 10: [Advanced] p. 341, Problem 4.32(c,d).

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Question 11: [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: jω ) = . 5 1 + jω-. 5 3 + jω , (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 12: [Basic] p. 346, Problem 4.35(b). No need to do the sketch. Question 13: [Basic] 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. As a result, they try to use a diﬀerent 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. Question 14: p. 631, Problem 8.22....
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## This note was uploaded on 02/05/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Fall '06 term at Purdue.

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HW9 - jω = 5 1 jω 5 3 jω(1 and use p 290 Example 4.1 Let...

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