Assignment #13 ECSE-2410 Signals & Systems - Spring 2009 Due Tue 03/17/09
1(20). Consider the signal x(t)=3cos(t)+2cos(3t)+cos(4t). (a) Find the Nyquist sampling frequency, s, which guarantees that x
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
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"
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 indi
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
otherw
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 graphic
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 Sectio
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
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
K
ECSE 2410 - Signals & Systems
September 8, 2014
a
Solution of Assignment 2
1. (a) According the sampling property of Delta function we have
t+
0
f (t)(t t0 )dt =
t
0
f (t)(t t0 )dt = f (t0 )
Therefore
ECSE 2410 - Signals & Systems
September 9, 2014
a
Solution of Assignment 3
1. Based on the denition of a(t) we have
t
d
a(t) = x(t)
dt
x( )d
a(t) =
d
d2
a(t) = x(t)
2
dt
dt
On the other hand, based on
ECSE 2410 - Signals & Systems
September 16, 2014
a
Solution of Assignment 5
1. (a) Output y1 [n] = x1 [n] h[n]. Based on which we construct the table as follows. Therefore
ECSE 2410 - Signals & System
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 p
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)
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
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) +
ECSE 2410 - Signals & Systems
September 2, 2014
a
Assignment 2
Due on September 5, 2014
1. Evaluate
(a)
e ( 2)d
(b)
t
e ( 2)d
(c)
t
e u( )d
2. Find the Laplace transform of x(t) given in the following