Signal and System
T.J
ECE124F17HW2.docECE 124 HOMEWORK #2
1. A CT SISO system having input
()
xt
and output()
yt
is described by the relationship
()log|(0.3)|
e
ytxt
=+
. Prove that the system is (or is not) linear, causal, time invariant, stable, memoryless.2. A DT SISO system having input
[]
xn
and output[]
yn
is described by the relationship
[][]
kn
ynxk
¥
=-
=
å
. Prove that the system is (or is not) linear, causal, time invariant, stable, memoryless.3. A CT SISO system having input
()
xt
and output()
yt
is described by the relationship2
/2
()(')'
t
ytxtdt
¥
=
ò
. Prove that the system is (or is not) linear, causal, time invariant, stable,memoryless, invertible.
4. Show that the CT SISO system having input
()
xt
and output()
yt
is described by the relationship1/3
3
0
()(')'
T
ytxttdt
æö
=-
ç÷
èø
ò
, where0
T
<<¥
, obeys the homogeneity property but not the additivity property. Show that the systems is (or is not) causal, stable, and time invariant.5. 2. A DT SISO system having input
[]
xn
and output[]
yn
is described by the relationship
[1]
[](5)
xn
yn
+
=
. Prove that the system is (or is not) linear, causal, time invariant, stable, memorylessNote:
Â
means the set of all real numbers andI
means the set of all integers.1
