s03_cgs - Approximation by Pulses Consider representing the...

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Approximation by Pulses Consider representing the smooth function, u ( t ) ,asa sum of pulses, rather than as a sum of steps, as in Duhamel’s Integral, as shown below: u(t) t τ 1 τ -3 τ -2 τ 4 τ 3 τ 2 τ 0 . . . τ -1 . . . Find an (approximate) expression for u ( t ) summation of scaled and delayed pulses. u ( t )= ? n = −∞ Hint: Express each pulse in terms of the unit step, σ ( · ) .
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Approximation by Pulses My confidence that I have the correct answer is: 1. 100% 2. 80% 3. 60% 4. 40% 5. 20% 6. 0%
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Approximation by Pulses The correct answer is u ( t ) u ( τ n )[ σ ( t τ n ) σ ( t τ n +1 )] n = −∞ My answer 1. Was completely correct 2. Was mostly correct, with one or two minor errors 3. Had many errors 4. Was completely incorrect
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General Response Consider the input u ( t ) to a system G , with step response g s ( t ) . The input u ( t ) is represented as a sum of pulses, as shown below: u(t) t τ 1 τ -3 τ -2 τ 4 τ 3 τ 2 τ 0 . . . τ -1 . . . The input signal is approximated as u ( t ) u ( τ n )[ σ ( t τ n ) σ ( t τ n +1 )] n = −∞
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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s03_cgs - Approximation by Pulses Consider representing the...

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