King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
( )
( )
( )
(
(
( )
( )
)
)
( )
( )
( )
(
(
( )
( )
 
(
( )
( )
( )
 ( )
Provided
exists, n is nonnegative
integer
Convolution in the time
domain
Multiplication in the
time domain
is real
( )
( )
)
Duality
Provided
(
Remarks
Linearity
is real
is real
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
@
['i) gridFt: ,Siaml T. S'i n (111?;1: JVI) 1:) ptrioJ :W5
0 Ba tatMa If. 05 Anti Hake. J. at. grid 0? m sigma.
Signal 'I'5 1355i; an} Hut. pcrioJ is, 35
(Elr) Sin (.13 ' 26% I? : Sin(211$_f I 265(11'l'l) =P'Ti 515E '..'.r:%l
:9 'r rail1:6 i
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
4:0 uCxefg Sefleig
14$.
Eawge
a um}?
QRQ¥CM¥ Cat/0 OLQa'KVc mnoncwkxtc C V's W15 5 EE rat
96» 9&1: Sbwmj 1W) / Ag?di cum one MQATD:
3)
\ a MA .
WP): ihx é
O _.~\ .1. "k x '1 1
357159.
+9 "T: 3
+00 _ LSLXL_ J I.)
WV): (WA EQnW§ Hugf) a: "t3
\ A 9
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Extra problem 1
Prove that for an LTI real system with frequency response
( )
 ( )
 ( )
(
( )
if the input is
(
), the output is
( )
Extra problem 2
Consider an LTI system with frequency response ( )
 ( )
( )
.
What is the output of the system in re
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
P1: RPU/XXX
P2: RPU/XXX
CUUK852Mandal & Asif
QC: RPU/XXX
May 25, 2007
T1: RPU
18:7
CHAPTER
1
Introduction to signals
Signals are detectable quantities used to convey information about timevarying
physical phenomena. Common examples of signals are human
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Chapter 5: Continuoustime Fourier Transform
Problem 5.1
(a)
The CTFT for x1(t) is given by
X 1 () =
jt
jt
[ t ] e dt + [1 t ] e dt
= 1+
[]
t
jt
2
2
=
(b)
[]
e
( j)
1
=
( j)
=
0
x1 (t )e jt dt = 1 +
[1 ]
( j)
2
( / 2)
2
+ 1
( j) 2
e
1
2 cos()
sin
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Chapter 4: Signal Representation using Fourier Series
Problem 4.1
(a)
Using Definition 4.4, the CT function x1(t) can be represented as x1(t) = c11(t) + c22(t) + c33(t)
with the coefficients cn, for n = 1,2, and 3, given by
T
c1 =
1
2T
x1 (t )1 (t )dt =
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Chapter 2: Introduction to Systems
Problem 2.1
(i)
The currents flowing out of node 1 along resistors R1, R2, and capacitor C, are given by
iR1 =
y (t ) v (t )
,
R1
iR 2 =
y (t )
,
R2
iC = C
dy
dt
Applying the Kirchoffs current law to node 1 and summing u
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Chapter 3: Time Domain Analysis of LTIC Systems
Problem 3.1
Linearity: For x3(t) = x1(t) + x2(t) applied as the input, the output y3(t) is given by
d n y3
dt n
+ an 1
d n 1 y3
+
dt n 1
+ a1
dy3
d m 1 (x1 (t ) + x2 (t )
d m (x1 (t ) + x2 (t )
+ a0 y3 (t )
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2014
Chapter 1: Introduction to Signals
Problem 1.1:
i) z[m,n,k] is a three dimensional (3D) DT signal. The independent variables are given by m, n, and k,
while z is the dependent variable. Digital video is an example of a 3D DT signal of the form z[m,n,k]. T
King Abdullah University of Science and Technology
signal and system
EE 151

Fall 2015
clear all
close all
clc
% Problem 1.2(iv)
t=linspace(1,2,1000);
% Define the time axis over the interval from 1 to 2. Use uniformly spaced
% points over the interval. If vector or array t is defined as linspace(a,b,N), then
% the N elements of t are giv