q3 - 6.003(Fall 2009 Quiz#3 Name Kerberos Username Please...

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6.003 (Fall 2009) Quiz #3 November 18, 2009 Name: Kerberos Username: Please circle your section number: Section Instructor Time 1 Marc Baldo 10 am 2 Marc Baldo 11 am 3 Elfar Adalsteinsson 1 pm 4 Elfar Adalsteinsson 2 pm Partial credit will be given for answers that demonstrate some but not all of the important conceptual issues. Explanations are not required and will not affect your grade. You have two hours. Please put your initials on all subsequent sheets. Enter your answers in the boxes. This quiz is closed book, but you may use three 8 . 5 × 11 sheets of paper (six sides total). No calculators, computers, cell phones, music players, or other aids. 1 2 3 4 5 Total / 12 / 20 / 18 / 25 / 25 / 100
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Quiz #3 / 6.003: Signals and Systems (Fall 2009) 2 1. Impulsive Input [12 points] Let the following periodic signal x ( t ) = m = −∞ δ ( t 3 m ) + δ ( t 1 3 m ) δ ( t 2 3 m ) be the input to an LTI system with system function H ( s ) = e s/ 4 e s/ 4 . Let b k represent the Fourier series coefficients of the resulting output signal y ( t ) . Deter- mine b 3 . b 3 =
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Quiz #3 / 6.003: Signals and Systems (Fall 2009) 3 Worksheet (intentionally blank)
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Quiz #3 / 6.003: Signals and Systems (Fall 2009) 4 2. System Design [20 points] Design a stable CT LTI system H with all of the following three properties: the impulse response h ( t )
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