HW 3: Solutions

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

• 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.