1
EECS20n, Solution to Midterm 1, 10/20/00
1.
10 points
The function
x
:
Reals
→
Reals
given by
∀
t
∈
Reals
x
(
t
)=s
in(2
π
×
440
t
)
is a mathematical example of a signal in the signal space
[
Reals
→
Reals
]
. Give mathematical
examples of signals in the following signal spaces.
(a)
(2 pts)
[
Ints
→
Reals
]
∀
n
∈
Ints
,x
(
n
)=
n
(b)
(2 pts)
[
Nats
0
→
EnglishWords
]
∀
n
∈
Nats
0
(
n
the
(c)
(2 pts)
[
Reals
→
Reals
2
]
∀
t
∈
Reals
(
t
)=(
t,
2
t
)
(d)
(2 pts)
[
{
0
,
1
,
···
,
600
}×{
0
,
1
,
,
400
}→{
0
,
1
,
,
255
}
]
∀
(
m,n
)
∈{
0
,
1
,
,
600
0
,
1
,
,
400
}
(
m
+
n
)
mod
255
(e)
(2 pts)
Give an example of a practical space of signals whose mathematical representa-
tion is
[
{
0
,
1
,
,
600
0
,
1
,
,
400
0
,
1
,
,
255
}
]
.
This is the appropriate signal space for images of size
600
×
400
pixels with an 8-bit
color map index.