toán kỹ thuật,lê minh cường,dhbkhcm Hw3 Fourier Transform [1] Homework3 Fourier Transform Prob3 1 Using table and properties of Fourier transform, compute F(ω) (a) f(t) = u(t – 1 ) – u(t – 2) (b) f(t)[.]
Trang 1 Homework3: Fourier Transform
Prob3.1: Using table and properties
of Fourier transform, compute
F( ω) :
(a) f(t) = u(t – 1 ) – u(t – 2)
(b) f(t) = 4 δ(t + 2)
(c) f(t) = e –4t u(t)
(d) f(t) = e –4t u(t – 2)
(e) f(t) = 2cos 2 (t)
Trang 2 Homework3: Fourier Transform
Prob3.2: Use the defining integral to find the Fourier transform
of the following functions:
f(t) A (0 / 2)
0 (
a
)
)
t t
elsewhere
τ
τ
− − < <
= < <
at
0 ( 0) f(t)
te (0 );
b)
a 0
t
t
−
<
=
< >
Trang 3 Homework3: Fourier Transform
Prob3.3: Use the defining integral to
find the Fourier transform of the
function:
e(t)
E m
– τ/2 0 τ/2 t
Prob3.4: Use the defining integral to
find the Fourier transform of the
function:
e(t)
0
t(s)
- 2
- 4
10
- 10
Trang 4 Homework3: Fourier Transform
Prob3.6: Given R 1 = 1 Ω, R 2 =
3 Ω, L = 1H, j(t) = 50cos(3t) A
Compute H(j ω) = I(ω)/J(ω) ? Use
Fourier transform to find i(t) ? Check the answer by using AC analysis ?
dervative:
f(t) 1
1 – 1
t(s) 0