Chapter 3 Problem Solution
Homework:
3.1 3.13 3.15 3.34 3.35
Chapter 3 Problem Solution
3.13 Consider a continuous-time LTI system
4s i n?jH
8t4 1
4t0 1 tx
000
tjk
k
k
ejkHaty
Chapter 3 Problem Solution
3.15
100 0
100 1
jHtxtyπ/Ttx S 6,
For what values of k is guaranteed that?0?
ka
0 8kak
3.35
o t h e r w i s e 0
250 1jHtxtyπ/Ttx S 7,
For what values of k is guaranteed that?0?
ka
0 1 8kak
Chapter 3 Problem Solution
3.34 Consider a continuous-time LTI system
Find the Fourier series representation of the output
for each of the following inputs,
4 teth
ty
nttx
n
( a )
nttx n
n
1 ( b )
(c) is the periodic wave depicted in Figure P3.34tx
1tx
-2 -1 0 1 2 t
2/1
Chapter 3 Problem Solution
0 0 0 0c os c osLt H j t H j
Hjyt
0cos t?
0sin t?
0 0 0 0sin sinLt H j t H j
t tths in?Consider an LTI system S with impulse response
Determine the output of S for the input
Suppose we are given
ntxtx
n
31
o t h e r s 0
11 1
1
t-tx
Chapter 3 Problem Solution
tty
3
2c o s3
2s i n2
3
2?
Homework:
3.1 3.13 3.15 3.34 3.35
Chapter 3 Problem Solution
3.13 Consider a continuous-time LTI system
4s i n?jH
8t4 1
4t0 1 tx
000
tjk
k
k
ejkHaty
Chapter 3 Problem Solution
3.15
100 0
100 1
jHtxtyπ/Ttx S 6,
For what values of k is guaranteed that?0?
ka
0 8kak
3.35
o t h e r w i s e 0
250 1jHtxtyπ/Ttx S 7,
For what values of k is guaranteed that?0?
ka
0 1 8kak
Chapter 3 Problem Solution
3.34 Consider a continuous-time LTI system
Find the Fourier series representation of the output
for each of the following inputs,
4 teth
ty
nttx
n
( a )
nttx n
n
1 ( b )
(c) is the periodic wave depicted in Figure P3.34tx
1tx
-2 -1 0 1 2 t
2/1
Chapter 3 Problem Solution
0 0 0 0c os c osLt H j t H j
Hjyt
0cos t?
0sin t?
0 0 0 0sin sinLt H j t H j
t tths in?Consider an LTI system S with impulse response
Determine the output of S for the input
Suppose we are given
ntxtx
n
31
o t h e r s 0
11 1
1
t-tx
Chapter 3 Problem Solution
tty
3
2c o s3
2s i n2
3
2?