Please find the zero-input response )( 0 ty of the following systems, if the initial conditions arey0 (0) = 1, and Dy0 (0) = −1.

ECE/355: Signals and Systems

Homework #3 Due day: 02/25/2019
1. Please find the zero-input response
( )
0
y t
of the following systems, if the initial

conditions arey0

(0) = 1, and Dy0

(0) = −1.

1).
( 7 10) ( ) ( )
2 2 D  D y t  D x t

2).
( 4 4) ( ) ( 1) ( )
2 D  D y t  D  x t
2. Please determine the unit impulse response

h(t) of the following systems

(Given:
h(t) b (t) [P(D)y (t)]u(t) 
n  n

):
1). ( 6 8) ( ) ( 2) ( )
2 2 D  D y t  D  x t
2). ( 4 4) ( ) ( 5) ( )
2 D  D  y t  D  x t

3. Using direct integration to calculate the following convolutions (Don’t use the
convolution table):
1).
e u(t)*e u(t)
at bt

2).
tu(t)*u(t)

4. Please use the convolution table to calculate following convolutions:

1).
( )*(1 ) ( )
2
e u t e u t
 t t

2).
[cos(5t) e ]u(t)* (2 t)

t
 

3).

( 3)*[ ] ( 1)
( 3) 2( 1) ( 1)
  
     
e u t e e u t
t t t

5. The unit impulse response of an LTIC system is

h(t) e u(t)
t

. Please use the

convolution table to find the zero-state response y(t) if the input is:
1).
x(t)   (t  5)
;

2).
x(t)  (t  4)u(t  4)
;

3).
( ) ( 1) +sin(3t)u(t)

image 316 - Please find the zero-input response )( 0 ty of the following systems, if the initial  conditions arey0  (0) = 1, and Dy0  (0) = −1.

image 317 - Please find the zero-input response )( 0 ty of the following systems, if the initial  conditions arey0  (0) = 1, and Dy0  (0) = −1.

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images - Please find the zero-input response )( 0 ty of the following systems, if the initial  conditions arey0  (0) = 1, and Dy0  (0) = −1.

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