Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
hap. 2
Sec. 2.5
Linear ConstantCoefficient Difference Equations
33
x[n] * ben] = x[n]. In this case, the backward difference system compensates exactly
for (or inverts) the effect of the accumulator, i.e., the backward difference system is the
inverse sy
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
PPye ub S m e s for the [email protected] FIR%=
(c) "purely recursive system"

2.5.2 Recursive and NonrecursJve ~ t z a t i o n s
of FIR
Systems
I;.  %
.
H
.
W e have already made the distinction between FIR and IIR systems, based on
w
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Tutorial4
Q.1
Prove that the area of a Gaussian function given by
f ( x)
1
2 2
e
x2
2 2
, x
is unity.
Q.2
Given that H ( f )
h(t )e
j 2 ft
dt , where h(t ) is a function of time and H ( f ) is a
function of frequency. Show that h(t )
H ( f )e
j 2 f
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet04
DAIICT, Gandhinagar.
1. Using the definition of linearity, show that the ideal delay system and moving
average (MA) system are both linear systems.
x n
Ideal Delay
(nd) System
y n T x n x n nd
Fig.1a. Ideal
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet10
DAIICT, Gandhinagar.
1. Find the Discretetime Fourier transform (DTFT) of
(a) x n 0.2 u n
n
2. Prove that the DTFT of discretetime signal x n , is periodic, i.e.,
X e
j 2
X e j
x n e
where, X e j
j
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet02
DAIICT, Gandhinagar.
1. For the following signals verify if they are of energy/power type. Accordingly
compute the energy and power of the signal over a duration of T seconds
(a) g (t ) Ae
j (2 f0t )
(b) g (
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet11
DAIICT, Gandhinagar.
1. Find the frequency response, H , of the causal and stable LTI systems which are
modeled by secondorder differential equations
d 2 y t
dy t
4
4 y t x t
2
dt
dt
d 2 y t
dy t
5
4
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet06
DAIICT, Gandhinagar.
1. If the systems shown in Fig. 1(a) and Fig. 1(b) are equivalent, find h n .
LTI system with
x n
LTI system with
n
n
1
h1 n u n
3
1
h2 n u n
6
y n
Fig. 1(a)
LTI system
with h n
x n
y
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet05
DAIICT, Gandhinagar.
Problem 1 Consider a linear timeinvariant (LTI) system whose response to the signal x1 t
in Fig. 1a is the signal y1 t in Fig. 1b. Determine and sketch carefully response of the system
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet13
DAIICT, Gandhinagar.
1. A signal x t undergoes a zeroorder hold operation with an effective sampling period
T to produce a signal xo t . Let x1 t denote the result of a firstorder hold operation
on the sam
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet08
DAIICT, Gandhinagar.
Problem 1: Consider a causal LTI system implemented as the RL circuit shown in
figure below. A current source produces an input current x(t ) , and the system output is
considered to be
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet01
DAIICT, Gandhinagar.
1. Represent following complex number in Zplane for
a) z1 = 1 + 2 j ,
b) z 2 = 1 2 j ,
1
1
c) z3 = 2cos 2 + j 2sin 2 ,
2
2
d) z4 = 3 cos 3 + j 3 sin 3 .
2. Multiplication by j
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Tutorial Class:7
SAS Autumn 2010
Fourier series representation
Problem 1: A continuoustime periodic signal f (t ) is real valued and has a fundamental
period T 8 . The nonzero Fourier Series coefficients for f (t ) are a1 a1 2 ,
a3 a3 4 j . Express f
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet03
DAIICT, Gandhinagar.
1. Determine and sketch the even and odd parts of the signals shown below in Fig.1
and 2.
x t
1
0
1
2
t
Fig. 1. A continuoustime signal
x n
1
1
0
1
2
3
4
5
n
Fig. 2. A discretetime si
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet09
DAIICT, Gandhinagar.
1. Find the Fourier transform of
(a) t 1 t 1
(b) e2t u t
3 t 1
(c) e u t 1
2. Consider a causal LTI system with frequency response
H j
1
.
4 j
For a particular input x t this system is
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and systems
Tutorial 2
1. Given the system be defined by the following equation
Y(t) = 2x(t)
Let us consider =2; =3
The input signals are as follows:
a) Plot the response of the system by applying
x1(t) + x2(t) as input
b) Plot the response by app
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and systems
Tutorial 3
CT203
1) Find the response of the system when a signal is passed through
a) Low pass filter
b) High pass filter
Note: Use Mat Lab to find the response
2)
Check whether the systems are causal or stable or both using the impul
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet13
DAIICT, Gandhinagar.
1. By computing the group delay at three selected frequencies, verify that the
1
frequency response H
has nonlinear phase characteristics.
j 1
2. Consider a discretetime lowpass filter
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Signals and Systems (CT 203)
Tutorial Sheet15
DAIICT, Gandhinagar.
1. Find the Ztransform of following sequences and plot their ROC
n
a) x n u (n 1)
b) x n nu (n)
c)
x n nu (n) bnu(n 1)
2. Find the Ztransform of
i) x1 n cos o n u (n)
ii) x2 n sin o n
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
CT 203: Signals and Systems
Tutorial on Fourier Transform and Hilbert
Transform
(Week of October 02, 2011)
1. Let g(t) = Aebt u(t). What are the range of frequencies that would contain x% of the total
energy of g(t)?
2. Using the duality theorem compute t
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and Systems
CT 203

Winter 2015
CT203 Signals & Systems
Autumn 201516, Maximum marks 40
End Semester examination
Friday, 27/11/2015, 14:00  16:30
1. Answer the following with a short justification.
[8 marks]
(a) Let z(t) = ( x y)(t), t R. Is the following statement True or False: The
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and Systems
CT 203

Winter 2015
CT203: Signals & Systems
Tutorial  1
Aditya Tatu
1. One may represent the following signals as functions f : X Y. Identify the domain
X and codomain Y for each of the following:
(a) Your mobile battery power over time.
(b) CPIs of students at DAIICT.
(
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
Analog Modulation Chapter 2
Example 2.4
For an AM modulator with a carrier frequency of 150 kHz and a modulating
signal frequency of lOkHz, determine the :
i) Frequency for the upper and lower sideband .
ii) Bandwidth.
Sketch the output frequency spectrum
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
294 Chapter Ten
Where transmission lines form the channel, the frequency response
of the lines also must be taken into account. With a satellite link, the
main channel is the radiofrequency path, which has little effect on the
frequency spectrum but does
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
I76
CHAPTER4 o Lineaer Mixtuiation
All of the foregoing expressions come from simple trigonometric expansions.
Clearly. in both DSB and 353. a frequency drift thats not small compared to W
will substantially alter the detected tone. The effect is more sev
Dhirubhai Ambani Institute of Information and Communication Technology
Signals and System
CT 203

Summer 2016
CHAPTER 12 O Digitization Techniques for Analog MeSsages and Computer Networks
done by correction or concealment in the following order. First we employ check
digits to correct errors that occur. If a specic bit is incorrect, we simply change it to
the