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Introductory Lecture-Digital Signal Processing-Lecture Slides, Slides of Digital Signal Processing

COMSATS Institute of Information Technology (CIIT)Digital Signal Processing

This lecture is part of lecture series delivered by Dr Muhammad Fasih Uddin Butt for Digital Signal Processing course at COMSATS Institute of Information Technology. Its main points are: Course, Rationale, Applications, Speech, Image, Multmedia, Processing, Learning, Oucomes, Signals, Linear, System

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EEE324
Digital Signal Processing
Instructor: Dr Muhammad Fasih Uddin Butt
Fall 2011
BET 5 (C)
Course Rationale
Digital Signal Processing (DSP) is used
everywhere, from Apple’s iPOD and iPhone or
the latest Zune, to the A380 Airbus.
Modern communication systems depend heavily
on DSP to deliver the various services that are
now offered.
Most modern cars cannot function without the
assistance of DSP processors.
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Partial preview of the text

Download Introductory Lecture-Digital Signal Processing-Lecture Slides and more Slides Digital Signal Processing in PDF only on Docsity!

EEE

Digital Signal Processing

Instructor: Dr Muhammad Fasih Uddin Butt

Fall 2011

BET 5 (C)

Course Rationale

„ Digital Signal Processing (DSP) is used

everywhere, from Apple’s iPOD and iPhone or

the latest Zune, to the A380 Airbus.

„ Modern communication systems depend heavily

on DSP to deliver the various services that are

now offered.

„ Most modern cars cannot function without the

assistance of DSP processors.

Applications of DSP

„ Speech processing

Enhancement – noise filtering

Text-to-speech (synthesis)

Recognition

„ Image processing

„ Multimedia processing

Media transmission, digital TV, video conferencing

„ Communications

„ Biomedical engineering

„ Navigation, radar, GPS

„ Control, robotics

Course Objectives

„ This course is designed to familiarize

students with the fundamental techniques

and applications of DSP.

„ This is achieved by teaching them the

relevant mathematical skills to describe,

analyze, and solve problems in DSP and

to evaluate and test the DSP systems

using software tools.

Text & References

Course Text:

Discrete-Time Signal Processing, Alan V. Oppenheim,

Ronald W. Schafer with J. R. Buck, Second Edition.

Reference Text:

Digital Signal Processing, Alan V. John, G. Proakis,

Dimitris, G. Manolakis, Third Edition.

Digital Signal Processing , Sanjit K. Mitra, Third Edition

Course Outline

„ Syllabus:

Signals and Systems, LTI systems, Fourier

Series, Fourier Transform => Ch. 2

Z-Transform => Ch. 3

Sampling => Ch. 4

„ Multirate signal processing

Transform analysis LTI systems => Ch. 5

Structures for Discrete-Time systems => Ch. 6

Filter Design Techniques => Ch. 7

The Discrete Fourier Transform => Ch. 8

Computation of DFT using FFT => Ch. 9

Theory Assessment Sessional I 10 Marks Sessional II 15 Marks Quizzes (3-4) 15 Marks Assignments(3) 10 Marks Terminal Exam 50 Marks Total 100 Marks Lab Work Assessment Labs (12) 70 Marks Labs Semester Project 30 Marks Total 100 Marks Final Grade: Theory/Labs = 75/25 %

Marks Distribution

NOTE:

Marks for each lab distributed between: (Attendance + Lab Performance + Report)

Credits 4(3,1)

Pre-requisites EEE 223

Semester 5

306

EEE 624 (1500-1800 hrs)

EEE 324 Digital Signal Processing 4(3,1)

307

EEE 324

417

417

Student Contact hours EEE 324

EEE 624 Adv Digital Signal Processing 3(3,0)

Course ID Course Title Cr Hrs.

Room # 417

1600 - 1800

Room # 305

Student Contact hours EEE 624

1430 - 1600 EEE 324

Room #

1300 - 1430

Room #

1130 - 1300

Room #

Research Day

Student Contact hours EEE 324

Research Day

1000 - 1130

Time MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

Weekly Schedule

List of Experiments (contd ..)

  1. Controlling Real-Time AM

Transmission/Reception parameters using

C6713 DSK

  1. Building a Simple I/O Audio Effect Processor

with C6713 DSK

  1. Designing a model of LMS Acoustic Noise

Reduction using C6713 DSK through Simulink.

  1. Semester Project/Lab viva
  2. Semester Project/Lab viva

Group home page:

http://groups.yahoo.com/group/ ciit_betf11_dsp

Group email address:

[email protected]

Signals

„ Broad definition: Functions of independent

variables.

Examples: music, velocity of some car, your cash, voltage or current in a circuit, your body temperature, your heart’s blood pumping rate..

„ Discrete in nature signals

Examples: Stock market indices, population statistics, average daily temperature

Analog and Discrete Signals

‰ An analog signal x(t) is a continuous

function of time; that is, x(t) is

uniquely defined for all t

‰ A discrete signal x(kT) is one that

exists only at discrete times; it is

characterized by a sequence of

numbers defined for each time, kT,

where

k is an integer

T is a fixed time interval.

Superposition Example

Additivity

„ y 1 = T{u 1 [n]}; y 2 = T{u 2 [n]}

„ y 3 = T{u 1 [n] + u 2 [n]} = y 1 [n] + y 2 [n]

Homogenity

„ ky 1 [n] = T{ku 1 [n]}

Non-linear Systems:

y[n] = x²[n] (i.e. T{.} = (.) ²)

T{x 1 [n] + x 2 [n]} = x 1 ²[n] + x 2 ²[n] + 2x 1 [n]x 2 [n]

Linear System T{.}

u 1 [n] + u 2 [n] y^1 [n]^ + y^2 [n]

Linear System a*u T{.} 1 [n]^ + b*u 2 [n]^ a*y^1 [n]^ + b*y^2 [n]

Linear Time Invariant System

„ A time-invariant system has properties unvarying

with time, i.e.:

if y[n] = T {x[n]}

implies

y[n-k] = T {x[n-k]}

„ Linear Time-invariant (LTI) system is a system

that is both linear and time-invariant (sometimes referred

to as a Linear Shift-Invariant (LSI) system)

Unit Step Function

The Unit Impulse Function

„ Dirac delta function δ ( t ) or impulse function is an

abstraction—an infinitely large amplitude pulse,

with zero pulse width, and unity weight (area

under the pulse), concentrated at the point where its argument is zero.

Transformations of time variable

„ Shifting

-ve shift

+ve shift

„ Flipping

„ Scaling

t

x(t)

x(-t)

t

t

x(2t)

t

x(t/2)

Superposition in LTI Systems

„ Exercise: Given response y(t) of an LTI system to the input signal x(t)

below, find response of that system to the input signals x 1 (t) and x 2 (t)

shown below.

x(t)

t

y(t)

t

x 1 (t)

1 t

x 2 (t)

t

Sifting property of δ(t)

„ x(t 0 ) is the weight of

the new scaled δ(t).

So x(t 0 ) has been

sifted out

X(t)

X(t 0 )

δ(t-t 0 ) 1

X(t 0 )

Causality

An LTI system is causal if and only if its impulse

response

∑

∑

∑

−

=−∞

∞

=

∞

=−∞

1

0

[ ] [ ] 0

y[n] [ ] [ ]

(i.e.,ifh[n] 0 forn 0)

y[n] [ ] [ ]

h[n] 0 forn 0

,

From thedefinition of acausal system

k

k

k

hk xn k

hk xn k

hk xn k

So

Stability

An LTI system is stable if

The system is stable if the output signal is bounded for all bounded

Input signals; called the bounded input-bounded output ( B I B O )

stability.

Let the input x[n] be bounded, as

Where M is a positive real finite number

∑

∞

=−∞

<∞ k

| h [ k ]|

| x [ n ]|≤ M

∑

∑

∑

∞

=−∞

∞

=−∞

∞

=−∞

k

k

k

M hk

hk xn k

yn hkxn k

| [ ] |

| [ ]|| [ ]|

| []| [][ ]

∑

∞

=−∞

k

| y [ n ]| if | h [ k ]|

Means for an LTI system to be stable its impulse

response is absolutely summable

∑

∞

=−∞

<∞ k

| h [ k ]|

Which is the necessary and sufficient condition.

Example: Is h[n] stable?

Thesystemisstableonlyfor|a| 1

1-|a|

|a |

seriesconvergesto

Fromamathematicalhandbook,theabovegeometric

|a | |a| 1 |a| |a| .....

computesum,

[] []

0

k

0

k 2 0

k

∑

∑ ∑

∞

=

∞

=

∞

=

k

k k

hn an^ un

Convolution Sum

Let h[n] be the response of the system to δ[n] Due to time-

invariance property, the response to δ[n-k] is simply h[n-k]

∫

∑ ∑

∑

∑

∑

∞

−∞

∞

=−∞

∞

=−∞

∞

=−∞

∞

=−∞

∞

=−∞

τ τ τ

δ

δ

yt h xt d

xn hn xkhn k hkxn k

xkhn k xn hn

xkT n k

T xk n k

yn T xn

k k

k

k

k

Foracontinuoussystem

[][] [][ ] [ ][ ] h[n]x[n]

Orderofconvolutionisnotimportant

[ ][ ] []*[ ]calledconvolutionsum

[ ]{ [ ]}

[][ ]

[] {[ ]}