ECSE 2410 - Signals & Systems
September 26, 2014
a
Assignment 8
Due on September 30, 2014
Note: We have used dierent notations for Fourier coecients in Section 1 and Section 2 of the
course. In Section 1, the Fourier coecients are denoted by ak , i.e.,
ak
ECSE 2410 - Signals & Systems
September 30, 2014
a
Assignment 9
Due on October 3, 2014
1. Consider the following three continuous-time signals with the fundamental period T = 1/2.
x(t) = cos(4t)
y(y) = sin(4t)
z(t) = x(t)y(t)
(a) Determine the Fourier ser
ECSE 2410 - Signals & Systems
October 3, 2014
a
Assignment 10
Due on October 7, 2014
1. For the circuit and input shown in Fig. 1,
Figure 1: Problem 1
(a) Show that if the input x(t) to an LTI system is periodic (expressed in terms of an
exponential Fouri
ECSE 2410 - Signals & Systems
October 17, 2014
a
Assignment 11
Due on October 21, 2014
1. Find the output y(t) of a system whose impulse response is h(t) = 3sinc(3t/2) and the input
is x(t) = cos(t) + cos(3t).
2. Find the Fourier transform of x(t) = M cos
Assignment #14
ECSE-2410 Signals & Systems Fall 2014
Due date 10/31/14
1(100). Consider the operations
x(t )
Ideal lowpass
filter
w(t )
Sampling,
2
T=5
x p (t )
Ideal reconstruction
filter
y (t )
Where the input signal is the periodic pulse train
x(t)
1
!
ECSE 2410 - Signals & Systems
October 21, 2014
a
Assignment 12
Due on October 24, 2014
1. We wish to transmit the signal
m(t) =
sin 103 t
t
by using amplitude modulation, which creates the signal
s(t) = (B + m(t) cos(104 t)
determine the largest permissib
ECSE 2410 - Signals & Systems
October 24, 2014
a
Assignment 13
Due on October 28, 2014
1. Show that the following is true.
eja ejb = 2jej
ab
2
sin
a+b
2
Start with the left side; then postulating the relationship
eja ejb = ejA (ejB ejB )
determine A and B
ECSE 2410 - Signals & Systems
October 31, 2014
a
Assignment 15
Due on November 4, 2014
1. Go through the derivation via Taylor series in the notes for
B(s) =
a0 + a1 s
b0 + b1 s + b2 s2
and nd the coecients a0 , a1 , b0 , b1 , b2 .
2. High order Butterwor
ECSE 2410 Signals & Systems
November 4, 2014
Assignment 16
Due on November 7, 2014
1. Design a 5th order Butterworth low-pass filter with a cutoff frequency (bandwidth)
of 10 KHz.
(a) Use Matlab or the web to find the five poles of the transfer function B
ECSE 2410 - Signals & Systems
November 7, 2014
a
Assignment 17
Due on November 11, 2014
1. Write the general form of the impulse response h(t) for the following pole-zero plots of H(s).
For example
represents h(t) = Ket .
2. A butterworth lowpass lter of
ECSE 2410 - Signals & Systems
November 11, 2014
a
Assignment 18
Due on November 14, 2014
1. Given
100
H() =
j 1 +
j
10
1+
j
50
(a) Sketch the straight-line Bode magnitude plot.
(b) Use the Bode magnitude approximation to calculate the approximate magnitud
ECSE 2410 - Signals & Systems
September 23, 2014
a
Assignment 7
Due on September 26, 2014
1. Signal c(t) is dened as c(t) = a(t) a(t) where
a(t)
1
t
1
1
1
(a) Find the convolution by using the graphical method
(b) Find the convolution by using Laplace tra
ECSE 2410 - Signals & Systems
September 16, 2014
a
Assignment 6
Due on September 23, 2014
1. Determine the convolution of the following two signals.
8
> t+1 0t1
>
>
<
f (t) =
2 t 1<t2
>
>
>
: 0
otherwise
g(t) = (t + 2) + 2 (t + 1)
2. For the two signals
f
ECSE 2410 Signals & Systems
November 7, 2014
Assignment 16
1. Design a 5th order Butterworth low-pass filter with a cutoff frequency (bandwidth)
of 10 KHz.
(a) Use Matlab or the web to find the five poles of the transfer function B() .
(b) Start with the
6*)
ECSE 2410 - Signals 85 Systems
0
ctober 31, 2014
_
Solution of Assignment 14
Pm'o cw'c -'°
(out
aha
11+)
{H
l
K='
7(a):
Rensselaer Polytechnic Institute
Fanfww (Sank/5
1: : aKea
K=-°°
165
L
AW
Kr:
,.
3-:
t
q:-
M swan)
ECSE Department ECSE 2410 - Sig
ECSE 2410 Signals & Systems
November 5, 2014
Solution of Assignment 15
ECSE 2410 Signals & Systems
November 5, 2014
Solution of Assignment 15
Problem 1. Continued.
ECSE 2410 Signals & Systems
November 5, 2014
Solution of Assignment 15
Problem 1. Continued
ECSE 2410 - Signals 85 Systems
Solution of Assignment 17
Rensselaer Polytechnic Institute 1
November 11, 2014
Pthw 11
_.
{E -1;
a) Hts): r- 2% Kc, ante) ~ka't)
(gar-+1
R2019 M U W
w an:
(3":0311-301
In W mth (1:1 w; Lori
H
K
b) H($).= .-2:-_ Q? cit-O, m
ECSE 2410 - Signals 85 Systems
December 2, 2014
Solution of Assignment 21
Rensselaer Polytechnic Institute
ProDLUWi'
#_._.
no _"-b -~(G'+LJ)'C voo -9;
a) S eh 6 <3 At _; S 8 At
0 0
mm d: '34;- (3"?5)
Pdt 0-0
vs: -3- 6
-OH:
'= 2: *1 *)
t=oo
Cammwbd)
ECSE 2410 - Signals & Systems
September 12, 2014
a
Assignment 5
Due on September 16, 2014
1. An LTI system has an impulse response h[n] = cfw_1, 1, 1, 0, . . . (Note that the rst 1 is
underlined indicating that this is the n = 0 value)
(a) Find output y1
ECSE 2410 - Signals & Systems
November 18, 2014
a
Assignment 19
Due on November 21, 2014
1. Given
x(t)
H(s)
K
y(t)
where
H(s) =
4
s(s + 4)
(a) In the s-plane nd and plot the locations of the close-loop poles for K = 1, 3, 5.
(b) Find the value of K so tha
ECSE 2410 - Signals & Systems
November 21, 2014
a
Assignment 20
Due on November 25, 2014
1. Consider the feedback system
!
X(s)%
+"
K!
G (s )
!"
Y(s)%
!
(a) Sketch the root locus.
(b) Calculate the value of s at the breakaway point (BAP).
(c) For what ran
ECSE 2410 - Signals & Systems
November 25, 2014
a
Assignment 20
Due on December 2, 2014
1. For each of the following integrals, specify the values of the real parameter which ensure
that the integral converges:
(a)
0 exp(5t) exp(
(b)
0
exp(5t) exp(
(c)
5
ECSE-2410: Signals and Systems
Final Exam - Fall 2016
Time: 150 Minutes
December 14, 2016
Name:
Solution
Section:
Exam Rules:
Please write your name on all your sheets.
Do not write your solution on the back side of the papers.
The exam papers will be s
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner