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HW 3: Solutions

HW 3: Solutions. The output of a particular system S is the time derivative of its input. Prove that system S is linear time-invariant (LTI). Solution:. HW 3: Solutions. HW 3: Solutions. What is the unit impulse response of this system? Solution:. d/dt ( (t)).  (t). 1/. 1/ 2.

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HW 3: Solutions

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  1. HW 3: Solutions • The output of a particular system S is the time derivative of its input. • Prove that system S is linear time-invariant (LTI). Solution:

  2. HW 3: Solutions

  3. HW 3: Solutions • What is the unit impulse response of this system? Solution: d/dt ((t)) (t) 1/ 1/2 unit impulseresponse unit impulse     t t -1/2 Limit as  tends to 0

  4. HW 3: Solutions Arbitrary LTI system Arbitrary LTI system d/dt d/dt y’(t) y’(t) x’(t) y(t) x(t) x(t) • Prove Property 5. That is, prove that, for an arbitrary LTI system, for a given input waveform x(t), the time derivative of its output is identical to the output of that system when subjected to the time derivative of its input. In other words, differentiation on the input and output sides are equivalent. Solution: Follows from Problem 1, and commutativity of convolution.

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