Review Problems
Convolution - Problem
The impulse response and the input to an LTI system are mentioned
below. Find the output y(t) of the system for the input x(t).
Fourier Series
Representation of
Periodic Signals
Fourier Series Representation
LTI systems are based on representing signals as linear
combinations of shifted impulses
We now examine an alternative representation for signals
and LTI systems
We represe
Introduction to System
and Types of Systems
System
Systems processes input signals to produce output signals
How Are Signal & Systems Related
How to design a system to process a signal in particular
ways?
Design a system to restore or enhance a particu
Digital Signal Processing
LAB
2
Discrete Time System and Classifications
A system is a collection of elements or components that are organized for a common
purpose. Physical systems in the broad sense are an interconnection of components, devices
or subsy
Digital Signal Processing
Lab 3
The Discrete-Time Fourier Transform
Fourier analysis is the study of the way general functions may be represented or
approximated by sums of simpler trigonometric functions.
If x(t) is a periodic function with period T, the
Properties of DTFT
In the previous lab two important properties of the DTFT were discussed that were
needed for plotting purposes. We now discuss the few other useful properties, which
are given below without proof.
Let X (ej) be the discrete-time Fourier
Digital Signal Processing
LAB 7
Real Time Signal Processing: Moving Average Filter
The moving average is the most common filter in DSP, mainly because it is the easiest digital
filter to understand and use. In spite of its simplicity, the moving average f
Digital Signal Processing
Lab 5
THE Z-TRANSFORM
As the discrete-fourier transform approches for representing discrete signals using complex
exponential sequences. And it has advantages for LTI systems becouse it describes systems
in the frequency domain u
Lab Tasks 1 and 2 for Lab &
Code:
t=0:0.001:4
t1=0:0.2:4
t2=0:0.5:4
t3=0:0.7:4
y=cos(2*pi*t)
y1=cos(2*pi*t1)
y2=cos(2*pi*t2)
y3=cos(2*pi*t3)
%Fs<2*Fc
subplot(3,1,1)
plot(t,y,'r')
hold on
plot(t1,y1)
%Fs=2*Fc
subplot(3,1,2)
plot(t,y,'r')
hold on
plot(t2,y2
NUST
COLLEGE OF ELECTRICAL AND MECHANICAL
ENGINEERING, RAWALPINDI
Digital Signal Processing
Lab Report # 1
Name: Ali Javed(6529)
Salman Arif(5909)
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 09/02/2016
TASK1:
Write a script or a function
NUST
COLLEGE OF ELECTRICAL AND
MECHANICAL ENGINEERING, RAWALPINDI
Subject Name: DSP
Lab Report Number: 3
Name: Salman Arif
Ali Javed
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 22-Feb-2016
1. Write MATLAB code to apply moving averaging f
NUST
COLLEGE OF ELECTRICAL AND MECHANICAL
ENGINEERING, RAWALPINDI
Digital Signal Processing
Lab Report No.5
Name: Ali Javed(6529)
Salman Arif(5909)
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 13/3/2016
Experiment #5:
Equalization through
NUST
COLLEGE OF ELECTRICAL AND MECHANICAL
ENGINEERING, RAWALPINDI
Digital Signal Processing
Lab Report # 4
Name: Ali Javed
Salman Arif
Degree: 35
Syndicate: A
Submitted to: Maam Ayesha Mehboob
Date: 02-03-2016
Experiment No. 4:
Learning Fast Convolution a
NUST
COLLEGE OF ELECTRICAL AND MECHANICAL
ENGINEERING, RAWALPINDI
Subject Name: DSP
Lab Report Number: 2
Name: Salman Arif
Ali Javed
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 15-Feb-2016
Experiment No. 2:
Convolution of Discrete Time S
NUST
COLLEGE OF ELECTRICAL AND
MECHANICAL ENGINEERING, RAWALPINDI
Subject Name: DSP
Lab Report Number: 6
Name: Salman Arif
Ali Javed
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 27-March-2016
Code:
w=-pi:pi/256:pi;
w0=0.4*pi;
n=0:100;
%/T
NUST
COLLEGE OF ELECTRICAL AND
MECHANICAL ENGINEERING, RAWALPINDI
Subject Name:
Lab Report Number:
Name: Salman Arif and Ali Javed
Degree: 35
Syndicate: A
Submitted to: LE Ayesha Mehboob
Date: 4 April, 2016
Task 1:
Lowpass
fvtool(lp);
Highpass:
fvtool(hp)
Complex Exponential
and Sinusoidal Signals
Discrete Time
Exponential Signals
a)
b)
c)
d)
Real Exponential signal x[n] = Aean; A and a are Real
a > 0 and A >0; exponential rise
a < 0 and A >0; exponential decay
a > 0 and A <0;
a < 0 and A <0;
How will (c
Fourier Series and its
Properties
Fourier Series of Periodic Square Wave
Fourier Series of Periodic Square Wave
The Fourier series of a square wave is a sinc function as
shown below:
Fourier Series of Periodic Square Wave
Magnitude of exponentials
Conver
Properties of LTI
Systems
Commutative Property
Hence the step response of an LTI system is the summation of its
impulse responses
Distributive Property
Associative Property
Associative Property
Memoryless and Identity LTI System
Invertible LTI System - DT
Discrete Time (DT)
Fourier Series
DTFS for Periodic Signals
There are only N different signals in the set of discrete-time complex
exponential signals
Since the exponential sequences are distinct only over a range of N
successive values of k, the FS summa
Properties of Fourier
Series
Properties of CTFS
We have studied the following properties of CTFS:
1. Linearity
2. Conjugate Symmetry
3. Time Shift
Now we will study the remaining properties:
1. Time Reversal
2. Time Scaling
3. Multiplication
4. Parseval
Complex Exponential
and Sinusoidal Signals
Continuous-Time
Motivation
These signals occur frequently in nature
They serve as basic building blocks from which we can
construct many other signals
Sinusoidal and periodic complex signals are used to
descr
Properties of Signals
Signal Properties
Continuous Time Periodic signals: A periodic continuous-time signal
x(t) has the property that for a positive value of time T,
x(t) = x(t + T), for all value of t.
Then x(t) is periodic with time period T.
The funda
Properties of Systems
System Properties
1.
2.
3.
4.
5.
6.
Memory
Invertible
Causal
Stability
Time Variance
Linearity
System Properties - Stability
A system is said to be bounded-input bounded-output stable
(BIBO stable or just stable) if the output signa
CT Convolution Problems
CT Convolution Problem 1
CT Convolution Problem 2
Evaluate y(t) = x(t) * h(t), where x(t) and h(t) are shown in
Figure below, (a) by an analytical technique, and (b) by a
graphical method.
Linear Time-Invariant
(LTI) Systems DT
Convolution
Linear Time-Invariant (LTI) Systems
Systems that are linear and time-invriant
Focus of most of this course
LTI systems are of practical importance
A basic fact: If we know the response of an LTI syste
Teachers Introduction
Dr. Salman Abdul Ghafoor
[email protected]
BSc Electrical Engineering,
UET Peshawar
MSc Electronic Communications,
University of Nottingham, UK
PhD Fibre Optic Communication,
University of Southampton, UK
Introduction to Si
CT Convolution
CT Signals as Sum of Impulses
Consider the staircase approximation,
( ), as shown below:
, to a CT signal,
It may be seen that the CT signal can be approximately
expressed as a linear combination of delayed pulses.
CT Signals as Sum of Im
Review Exercise
Periodicity
Draw the signal below and determine whether it is periodic
or not? If the signal is periodic, what is the fundamental
period?
x[n] =
4
[ 14 ]
Even and Odd Decomposition
Determine and sketch the even and odd parts of the sign