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# presec9 - ECE 2200 Section IX Problems(Week 10 Spring 2009...

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ECE 2200: Section IX Problems (Week 10 / Spring 2009) Note: In this section, we have ﬁve problems. Majority of the problems are taken from the ”Signal Processing First CD”, but they may have been slightly changed or may have some extra parts . Please read this handout carefully. Answers to all of the problems will be provided. 1. Use linearity and time-invariance to convolve the following two rectangular pulses: x ( t ) = 2 u ( t ) - 2 u ( t - 2) h ( t ) = 3 u ( t - 5) - 3 u ( t - 1) . (a) Expand the convolution y ( t ) = x ( t ) * h ( t ) into four terms and exploit the result from Example 9 - 9 from McClellan, Schafer and Yoder, Signal Processing First textbook to get y ( t ). (b) Write the answer for y ( t ) as separate cases over ﬁve diﬀerent regions. (c) Plot x ( t ) versus t , and y ( t ) versus t . 2. Signal Processing First CD: ”Chapter 9/Homework/Evaluating a Convolution In- tegral” A linear time-invariant system has impulse response: h ( t ) = ( e - 2 t - 1 t 1 0 otherwise

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presec9 - ECE 2200 Section IX Problems(Week 10 Spring 2009...

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