Signal and System
ECE 124 HOMEWORK #2
1. A CT SISO system having input
image1.wmf
()
xt
and outputimage2.wmf
()
yt
is described by the relationship
image3.wmf
()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
image4.wmf
[]
xn
and outputimage5.wmf
[]
yn
is described by the relationship
image6.wmf
[][]
kn
ynxk
¥
=-
=
å
. Prove that the system is (or is not) linear, causal, time invariant, stable, memoryless.3. A CT SISO system having input
image7.wmf
()
xt
and outputimage8.wmf
()
yt
is described by the relationshipimage9.wmf
2
/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
image10.wmf
()
xt
and outputimage11.wmf
()
yt
is described by the relationshipimage12.wmf
1/3
3
0
()(')'
T
ytxttdt
æö
=-
ç÷
èø
ò
, whereimage13.wmf
0
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
image14.wmf
[]
xn
and outputimage15.wmf
[]
yn
is described by the relationship
image16.wmf
[1]
[](5)
xn
yn
+
=
. Prove that the system is (or is not) linear, causal, time invariant, stable, memorylessNote:
image17.wmf
Â
means the set of all real numbers andimage18.wmf
I
means the set of all integers.1