Principles of Communication
Prof. V. Venkata Rao
CHAPTER 7
Noise Performance of Various Modulation
Schemes
7.1 Introduction
The process of (electronic) communication becomes quite challenging
because of the unwanted electrical signals in a communications
EE 220: Signals, Systems & Networks
Tutorial-2 Solutions
1. (a) x(t) = cos(t) , <t<
y(t) = |x(t)|2
= cos2 (t)
1 cos(2t)
=
+
2
2
Frequency components in output y(t) are d.c and 2rad/sec, where as
frequency in x(t) is 1rad/sec system is not an LTI.
(b)
y(t)
1. If a periodic signal f (t) with a period T0 satises the half-wave symmetry condition, then show that
all even numbered harmonics vanish and that the odd numbered harmonic coecients are given by
an
bn
=
=
4
T0
(T0 /2)
4
T0
(T0 /2)
f (t) cosn0 t dt and
EE 220: Signals, Systems & Networks
Tutorial-2
1. A fundemental property of LTI system that whenever the input of the
system is a sinusoid of certain frequency,the output will also be a sinusoid of the same frequency but with amplitude and phase determine
EE 350 : Control Systems
Date : 26.09.2014
(Show necessary steps)
Exchange of Calculators is not allowed
Mid-Semester Examination
July-Nov 2014
Marks : 30
Time: 2Hours
Q.N.1. (a) The block diagram of a feedback control system is shown in Fig.1(a). Find
di
EC-220: Signal, Systems and Networks (Quiz-1)
Q:
Consider an LTI system whose response to the signal x1(t) in Fig. 1 is the signal y1(t) illustrated
in Fig. 2. Determine and sketch carefully the response of the system to the input x2(t) in Fig.
3
1
EC220
Financial Accounting- An Overview
Faculty: K.S.Ranjani
Email: ksranjani99@gmail.com
Course Objective:
To orient students to accounting, make them aware of the basic concepts in accounting,
enabling them to understand the accounting process and understandi
GENERAL LEDGER AND TRIAL BALANCE
General Ledger & Trial Balance
INRODUCTION TO TRIAL BALANCE:
A businessman closes and balances the ledger accounts at the end of the month or year to prepare the trial balance.
Normally, he prepares the trial balance at th
Chapter 2
Signal Spaces
Language makes a mlghty loose net w ~ t hwhlch to go fi\hlng for srmple facts, when
facts are infinlte
- Edward Abbey
Desert Sohtaire
Begrnner5 are not prepared for real mathemat~calngor. they would see In ~t noth~ngbut
empty, ted~
Time-domain Analysis of CT and
DT Systems
Dr. R. Sinha
Dept. of Electronics & Communication Engineering
IIT Guwahati
Analysis of Continuous-Time
Systems
System Response
Consider a LTI system for which input x(t ) and output y (t ) are
related by linear di
Fourier Series Representation
Dr. R. Sinha
Dept. of Electronics & Communication Engineering
IIT Guwahati
The Continuous-Time Fourier
Series
Systems
Broadly speaking, a system is anything that
responds when stimulated or excited
The systems most commonly
Fourier Transform
Dr. R. Sinha
Dept. of Electronics & Communication Engineering
IIT Guwahati
Continuous-Time Fourier Transform
Extending the CTFS
The CTFS is a good analysis tool for systems
with periodic excitation but the CTFS cannot
represent an aperi
Laplace Transform
Dr. R. Sinha
Dept. of Electronics & Communication Engineering
IIT Guwahati
Introduction
There are two common approaches to the
developing and understanding the Laplace
transform
It can be seen as a natural consequence of the
fact that
f (t)
fi (t) (i = 1, 2, 3, 4, 5)
1
0
t
0
t
1
t
1
0
f4 (t)
1
f3 (t)
1
f2 (t)
1
0
1
f1 (t)
1
1
1 j
(e jej 1)
2
F () =
f (t)
0
1
2
t
1
f5 (t)
1.5
0
1
2
2
t
t
2
f (t)
cos10t
1
1
t
0
0
t
3
(a)
(b)
1
0
t
3
cos10t
(c)
Tutorial 12
22/4/16
1. The PSD of a Gaussian random process cfw_ X (t ) with non-negative mean is as shown in
Fig. 1
(a) Find the mean X , the autocorrelation function RX ( ) and the autocovariance
function C X ( ) of the process. Hence find the first-ord
Random Processes
Saravanan Vijayakumaran
sarva@ee.iitb.ac.in
Department of Electrical Engineering
Indian Institute of Technology Bombay
April 5, 2013
1 / 11
Random Process
Definition
An indexed collection of random variables cfw_Xt : t T .
Discrete-time R
EE 220: Signals Systems & Networks
Tutorial-8
1. Find the DTFT for the signals shown in the Fig. 1.
Figure 1:
2. (a) Show that the time expanded signal
x[n/L] n = 0, L, 2L, .
0
otherwise
xe [n] =
can also be expressed as
x[k][n Lk].(1)
xe [n] =
k=
1
(b) F
EE 220: Signals, Systems & Networks
TUTORIAL-10
Q.No.1: With the following facts about a discrete-time signal x[n] with z-transform
X(z):
1. x[n] is real and right-sided.
2. X(z) has exactly two poles.
3. X(z) has two zeros at the origin.
1
4. X(z) has a
EE 220: Signals Systems & Networks
Tutorial V
1. Consider an LTI system with input x(t), output y(t) and impulse response
1
h(t). If X(s) = s+2 ,x(t) = 0,t > 0 and y(t) = 2 e2t u(t) + 3 et u(t).
s2
3
(i) Determine H(s) and its ROC.
(ii) Determine h(t).
2.
EE 220: Signals, Systems & Networks
Tutorial-3 Solutions
Soln .1 :
1
1
2
-2
0
-1
1
1
2
3
-1
0
1
2
3
4
Figure 1:
Since m (t) = y (t) c (t) =
y ( )c (t
) d
y( ) and c( ) are shown in Figure 1. It is clear that
y( )c(t ) = 0 for t < 2 and t > 6 Therefore m
EE220: SIGNALS, SYSTEMS & NETWORKS
TUTORIAL-1
1. Do the reection and the time shifting operations commute? That is, do the two block diagrams in Figure 1 provide identical signals (i.e., is y(t) equal to z(t)? To provide the answer
to this, consider the s
EE220: Signals, Systems & Networks
Tutorial-9
1. Consider a system consisting of the cascade of two LTI systems with frequency responses H1 ej =
2ej
and H2 ej = 1 1 ej1+ 1 ej2 .
1+ 1 ej
2
2
4
(a) Find the dierence equation describing the overall system.
(
EE 220: Signals Systems & Networks
Tutorial IV: Solutions
1. For half wave symmetry we have
f (t) = f (t T0 /2)
T0
2
an =
T0
f (t)cos(n0 t)dt
0
T0
2
2
=
T0
Let t = t
T0
2
f (t)cos(n0 t)dt +
0
2
T0
T0
T0
2
f (t)cos(n0 t)dt
dt = dt (Substitute in second i
EE 220: Signals Systems & Networks
Tutorial 10: Solutions
1. From Clue 1, we know that x[n] is real. Therefore, the poles and zeros of
X(z) have to occur in conjugate pairs. Since Clue 4 tells us that X(z) has
1 j
a pole at z = 2 e 3 , we can conclude tha
Springer Series in
Computational
Mathematics
Editorial Board
R. Bank
R.L. Graham
J. Stoer
R. Varga
H. Yserentant
For further volumes:
http:/www.springer.com/series/797
42
Wolfgang Hackbusch
Tensor Spaces and Numerical
Tensor Calculus
123
Wolfgang Hackbusc
FUNCTIONAL ANALYSIS
PIOTR HAJLASZ
1. Banach and Hilbert spaces
In what follows K will denote R of C.
Definition. A normed space is a pair (X, k k), where X is a linear space
over K and
k k : X [0, )
is a function, called a norm, such that
(1) kx + yk kxk
Linear and Bilinear Functionals
October 6, 2010
1
Linear functionals
Definition 1. A real linear functional is a mapping l (v) : V R that is linear with respect to its argument v V.
That is, it must satisfy the properties
l (u + v) = l (u) + l (v)
l (v) =
Tensorlab Demos
Release 3.0
Otto Debals
Frederik Van Eeghem
Nico Vervliet
Lieven De Lathauwer
This is a demo-based introduction to tensor computations using Tensorlab.
The demonstrations
range from basic tensor operations, over multidimensional harmonic r
Bilinear Forms
Eitan Reich
eitan@mit.edu
February 28, 2005
We may begin our discussion of bilinear forms by looking at a special case that we are
already familiar with. Given a vector space V over a field F , the dot product between two
elements X and Y (