Biomedical Engineering Reference
In-Depth Information
1
0
_
ππ
−
20
π
−
10
π
10
π
20
π
t
(a)
1
4
2
0
2
4
−
π
−
π
π
π
t
(b)
FIGURE 11.42
f(t)
1
1
2
-
1
FIGURE 11.43
15.
Find the Fourier transform of
(a)
u(t)
e
at
u(t)
(c)
cos(
(b)
)
16.
Find the Fourier transform of
at
)
u
(
t
f
1
ð
t
Þ¼
e
3
t
u
ð
t
Þ
.
f
ð
t
Þ¼
e
3 jj
and sketch its time and frequency domain
representations. (Hint: Find a few points on the curve by substituting values for the variable.)
18.
Prove the shift property of the Fourier transform.
19.
Given x(
17.
Find the Fourier transform of
e
bt
u(t), where a and b are constants greater than zero,
explain why it would be easier to evaluate the convolution
e
at
u(t) and
t
)
¼
h
(
t
)
¼
) in the frequency domain.
20.
A brief current pulse of duration 50 ms and amplitude 1 mA is presented to a cell membrane
with time constant 10 ms. Find the cell membrane voltage output.
x
(
t
)*
h
(
t
Continued
