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Consider a causal linear and time-invariant (LTI) system whose response to the input x(t) = e−tu(t) is the output y(t) = (e−t + 2te−t − e−2 t)u(t). (3 points) Find the frequency response H(jω) of the causal LTI system. (3 points) Determine the linear constant-coefficient differential equation relating the input and output of this causal LTI system. (3 points) Find the unit-impulse response h(t) of the causal LTI system. (2 points) Find the unit-step response s(t) of the causal LTI system.

Consider a causal linear and time-invariant (LTI) system whose response to the input x(t) = e−tu(t) is the output y(t) = (e−t + 2te−t − e−2 t)u(t). (3 points) Find the frequency response H(jω) of the causal LTI system. (3 points) Determine the linear constant-coefficient differential equation relating the input and output of this causal LTI system. (3 points) Find the unit-impulse response h(t) of the causal LTI system. (2 points) Find the unit-step response s(t) of the causal LTI system.

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(11 points) Consider a causal linear and time-invariant (LTI) system whose response to the input x ( t ) = e − t u ( t ) is the output
y ( t ) = ( e − t + 2 t e − t − e − 2 t ) u ( t ) .
  1. (3 points) Find the frequency response H ( j ω ) of the causal LTI system.
  2. (3 points) Determine the linear constant-coefficient differential equation relating the input and output of this causal LTI system.
  3. (3 points) Find the unit-impulse response h ( t ) of the causal LTI system.
  4. (2 points) Find the unit-step response s ( t ) of the causal LTI system.

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