PROGRAM STUDI TEKNIK BIOMEDIS STEI-ITB
UJIAN TENGAH SEMESTER EB2205 SINYAL, SISTEM, DAN KONTROL
SEMESTER II 2021/2022 (Dosen: A. F. Masud)
Sabtu, 20 Maret 2022, 150 menit. Boleh Buka Catatan 1 lembar A4
Semua (5 buah) soal masing-masing berbobot sama
Soal 1
In Figure 1, a system shown with input signal x(t) and output signal y(t). The input signal
has Fourier transform X(j) shown in Figure 2
(a) Let V(j) be the Fourier Transform of v(t), sketch and clearly label V(j)
(b) Let R(j) be the Fourier Transform of r(t), sketch and clearly label R(j)
(c) Let S(j) be the Fourier Transform of s(t), sketch and clearly label S(j)
(d) Sketch and clearly label Y(j).
1
v(t)
x(t)
r(t)
1
s(t)

-5w -3w
cos(5wt)

3w 5w
Figure
Figure 11
-3w
y(t)
3w
cos(3wt)
X ( j )
1
Figure 2

-2w
0
2w
Figure 2
1
Soal 2
Consider the following two continuous time (CT) signals x(t) and h(t) as shown in Figure 3.
Figure 3
The signal y(t) is defined as the convolution y(t) = x(t) * h(t).
a. Compute y(t) = x(t) * h(t).
b. Provide a labeled sketch of y(t)
c. For what value (or values) of t is y(t) non-zero ?
d. For what value (or values) of t is y(t) maximum ? What is the maximum of y(t) ?
2
Soal 3
Let X(ejω) denote the Fourier transform of the signal x[n] depicted in Figure 4.
a. Find X(1) = X(ej0)
b. Evaluate

  X (e

c.
d.
e.
f.
j
)d
Find X(ejπ)
Find α such that ejαω X(ejω) real
Determine and sketch the signal whose Fourier transform is Re{ X(ejω) }
Evaluate each of the following integrals
(1).



(2).



2
X ( e j  ) d
2
dX (e j )
d
d
x [n]
1
2
1
0
5
2
3
4
6
7
8
9
10
11
Figure 4
3
Soal 4
Let x[n] be a periodic DT signal with a period of 10 depicted below
Figure 5
and let g[n] = x[n] – x[n-1]
a. Show that g[n] has a fundamental period of 10
b. Determine the Fourier series coefficients ak of the signal x[n]. Determine also a0
c. Determine the Fourier series coefficients bk of the signal g[n] . Determine also b0
4
Soal 5
Consider Figure 6. Express signals xa(t), xb(t), xc(t), xd(t), xe(t) in terms of signal x(t) and its timeshifted, time-scaled or time-reversed versions
x(t)
Figure 6
5