Assignment #5 – p.1
ECSE-2410 Signals & Systems - Spring 2007
Due Fri 02/02/07
1(20). Carry out the convolution,
)
(
)
(
)
(
t
w
t
v
t
y
∗
=
, of the signals shown, and sketch your result.
Study
the relationships between these examples to determine the general principles involved.
(a)
(b)
(c)
(d)
2(25).
This example illustrates the distributive property of convolution, namely, that convolution
distributes over addition:
(
)
)
(
)
(
)
(
)
(
)
(
)
(
)
(
2
1
2
1
t
h
t
x
t
h
t
x
t
h
t
h
t
x
∗
+
∗
=
+
∗
.
For the system shown, let
)
1
(
)
(
)
(
)
(
2
1
−
−
=
=
t
u
t
u
t
h
t
h
.
Determine and sketch
(a)
(b)
)
(
)
(
2
1
t
h
t
h
+
(
)
)
(
)
(
)
(
2
1
t
h
t
h
t
x
+
∗
Now find and sketch
(c)
(d)
)
(
)
(
1
t
h
t
x
∗
)
(
)
(
2
t
h
t
x
∗
(e)
)
(
)
(
)
(
)
(
2
1
t
h
t
x
t
h
t
x
∗
+
∗
You should be able to show that the sketches in (b) and (e) are the same.
0
2
t
)
(
1
t
v
)
(
1
t
w
t
0
2
1
1
4
0
2
t
)
(
2
t
v
)
(
2
t
w
1
1
t
0
2
4
0
2
t
)
(
3
t
v
)
(
3
t
w
1
1
t
4
0
2
4
0
2
t
)
(
4
t
v
)
(
4
t
w
1
1
t
0
2
)
(
1
t
h
)
(
2
t
h
+
+
)
(
)
(
t
u
t
x
=
)
(
t
y

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*