20082ee102_1_HW-3 - (i e-2 t sinh(5 t U t(ii e-t cos t-π 3...

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EE102: SYSTEMS & SIGNALS
HW: # 3
A LATE HW IS NEVER A HW!
Posted: April 17 Hand In: April 24
Attach This Sheet To Your HW
1. the IPOP relationship of a system S is
y ( t ) =
Z
t
-∞
x ( τ ) dτ +
Z
∞
t
e
t
e
( - τ )
x ( τ ) dτ, -∞ < t < ∞
Write down the IRF h(t) and the USR(Unit Step Response) g(t) of the
system.
2. The IPOP relation of a SISO system S is:
x ( t ) -→ [ S ] -→ y ( t )
y ( t ) =
Z
t
-∞
e
- ( t - τ )
x ( τ ) dτ, t ∈ ( -∞ , ∞ ) .
Write down the IRF h ( t, τ ) of S. Then compute its output y(t) given that its
input x(t) is
x ( t ) = e
- ( t - 1)
U ( t - 1) + U (2 - t ) , t ∈ ( -∞ , ∞ ) .
Hints: Decompose x ( t ) into x
1
( t ) + x
2
( t ) .
3. Calculate the Laplace Transforms of those functions on the Table(in the
Text) which have NOT been calculated for you in class. In each case clearly
indicate the DOC on the PZP of the transform.
1

4. Find the Laplace Transform of the following signals: