29883125 digital signal processing

7/27/2019 29883125 Digital Signal Processing

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DIGITALSIGNALAND

IMAGEPROCESSING

INTRODUCTION TO SIGNALS AND SYSTEMS

SIGNAL: -

A signal is defined as any physical quantity that varies with time, space or any

other independent variable or variables. It may be a function of one or more

independent variables. The signal itself carries some kind of information available for

observation.

Usually signals are classified into two types

Signals

Analog signals Discrete signals

(Continuous signals) ( Dis continuous signals)

ANALOG SIGNALS: - The analog signals are continuous function of an independent

variable such as time, space etc.

Ex:-

DISCRETE SIGNALS: -

1

x t

t


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A discrete signal is a function of a discrete independent variable, which is

an integer. A digital signal is same as discrete signal except that the magnitude of the signal is

quantized.

Ex:-

CLASSIFICATION OF DISCRETE TIME SIGNALS:

The discrete time signals are classified depending on their characteristics.

Some ways of classifying discrete signals are

z Energy signals and power signalsz Periodic and a periodic signalsz Symmetric and anti-symmetric signals

SYSTEMS:

DEFINITION: - A physical device that performs certain operations on a signal. Usually

systems are classified into two types.

Analog systems Digital systems

Comparison between analog and digital systems

ANALOG SYSTEMS DIGITAL SYSTEMS

1 Implemented by using RLC componentsImplemented by using delay unit,

multiplier and adders.

2 Accuracy is less Accuracy is more

3 More expensive Less expensive

4 Not flexible Flexible since be can increase the

order of systems by using feedback.

5 Not immune to noise. Hence less reliable

Signals are coded and transmitted.

Hence more immune to noise and

more reliable.

6 Difficult to store and retrieve. Easy to store

x(t)

t1 2 3 4


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7 High frequency signals can be used.

Limited range of frequency signals

are processed. Because of presence

of digital to analog converter.

8Consumes more power due to presence of

resistances

Consumes less power

9

Components like RLC available in standard

values.

Ex: If we require 76.8 ; resistor, we have to use

nearest values

No such restrictions.

Ex: If 16 bit processor is not giving

accurate value we can go for 32 bit

processor

For these reasons now a days all analog systems are replaced by digital systems

except for high frequency applications.

DISCRETE TIME SYSTEMS:

DEFINITION:

A discrete time system is a device or an algorithm that operates on a discrete

time input signal x(n), according to some well defined rule, to produce another discrete time

signal y(n) called the output signal. The relation ship between x(n) and y(n) is

y(n) = T[x(n)]

CLASSIFICATION OF DISCRETE TIME SYSTEMS:

Discrete time systems are classified according to their general properties and

characteristics. They are

STATIC AND DYNAMIC SYSTEMS: -A discrete time system is called static or memory less if its output at any

instant n depends at most on the input sample, at the same time, but not on part orfuture of the input. Otherwise system is dynamic system.

TIME VARIANT AND TIME INVARIANT SYSTEMS: -A system is said to be time-invariant if its input output characteristics do

not change with time. If y(n k) = H[x(n k)] system is time invariant otherwise

time variant systems.

DISCRETE-TIME SYSTEMx(n) y(n)


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CAUSAL AND NON-CAUSAL SYSTEMS: -A system is said to be causal if the output of the system at any time n depends

only on the present input, past input. Otherwise system is non-causal.

STABLE AND UNSTABLE SYSTEMS: -An arbitrary relaxed system is said to be BIBO if and only if every bounded

input produces a bounded output. If the output is unbounded, the system is classified

as unstable.

A linear system is one that satisfies superposition principle. It states that

the response of the system is equal to the weighted sum of all individual input

signals. Other wise system is said to be non-linear system.

FIR AND IIR SYSTEMS:In FIR systems, the impulse response consists of finite no. of samples. In

IIR systems, the impulse response consists of infinite no. of samples.

RECURSIVE AND NON RECURSIVE SYSTEMS:A system whose output Y(n) at time n depends on any no. of past output

values is called recursive system. A system where output depends only on the

present and past input is called a non-recursive system.

MEANING OF PROCESSING

DEFINITION: - It is mathematical operations carried out on the signal to extract

information.

Example: - Integration, differentiation, filtering etc.

ADVANTAGE OF PROCESSING: -

h(n)

n0

h(n)

n

0

Stable System Unstable System


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Using integrator an acceleration function can be converted into velocity

function can be converted into velocity function and a velocity function can be

converted into displacement function.

INTRODUCTION TO DIGITAL SIGNAL PROCESSING

Digital signal processing is the processing of signals by digital systems. The digital

systems are software, hardware or firmware. The purpose of such processing may be to

estimate characteristic parameters of a signal or to transform a signal into a form, which is

in some sense more desirable.

Signal processing problems are not confined of course to one-dimensional signals.

Many picture-processing applications require the use of two-dimensional signal-

processing techniques. The rapid development in the area of digital signal processing is a

result of the significant advances in digital computer technology and integrated circuit

fabrication. The rapid developments in integrated circuit technology, starting with

medium-scale integration and processing to large scale integration and very large scale

integration of electronic circuits has made the development of powerful, smaller, faster

and cheaper digital computers and special purpose digital hardware. In particulars, digital

signal processing hardware allows programmable operations. Through software, one can

more easily modify the signal processing functions to be performed by the hardware.

Thus digital hardware and associated software provide a greater degree of flexibility in

system design. Digital processors also form as integral part of many modern radar and

sonar systems.

COMPONENTS OF DIGITAL SIGNAL PROCESSORS: Any digital signalprocessor can be designed by using delay elements, multipliers and adders or

summers.

TYPES OF DIGITAL SIGNAL PROCESSORS: Digital Signal Processors areof two types

ANTI-ALIASINGFILTER

SAMPLE

+HOLD

A/DCONVER

TERDSP

D/A

CONVERTER

RECONSTRUCTION

FILTER

x(t) y(t)

fig: DIGITAL SIGNAL PROCESSING SYSTEM


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GENERAL PURPOSE PROCESSOR: These processors are used forany type of algorithm; usually they are bulk in size.

Dedicated processor: These processors are fast and small in size. Butthese are not used for different algorithms.

DISCRETE TIME FOURIER TRANSFORM AND Z-TRANSFORM

DISCRETE TIME FOURIER TRANSFORM: The Fourier transform ofdiscrete time signals is called discrete time Fourier transform. The Fourier

transform of a finite energy discrete time signal, x(n) is defined as

x(w) = x(n) exp(-j[n)

Ex:- Discrete in Time & A periodic Continuous in frequency & Periodic

n -2T -T 0 T 2T

Note: The Fourier transform of a signal is said to be existed if | x(n) | < E

Limitations of Discrete Time Fourier Transform:DTFT can be applied only to stable systems, since it exists only if the

impulse response is absolutely assumable, DTFT does not converge for all

sequences and it is useful to have a generalization of Fourier transform, z

transform is used.

Z- TRANSFORM: The z- transform of a sequence is defined asx(z) = x(n)zn

NEED OF Z-TRANSFORM IS DISCRETE TIME SYSTEMS:The z-transform is the appropriate transformation for discrete time systems. It is

counter part of lap lace transform, which is meant for continuous time signals. Z-

transform play an important role in the analysis and representation of discrete time

LTI system. Z transform of the impulse exists even for unstable systems. Thus z

transform can be used to study a much larger class of systems and signals.

n = -E

E

x(n) x([)

n = -E

E

n = -E

E


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PROPERTIES OF Z-TRANSFORM:

SL.

NOPROPERTY SHORT HAND NOTATION ROC

1 Linearity ax(n) + by(n)m ax(z)+by(z) R1 R2

2 Time shifting x(n-n0) m z-n0 x(z) R1

3 Frequency shifting ejPn

x(n) m x(ejPnz0) R1

4 Time reversal x(-n)m x(1/z) 1/R1

5 Convolution x(n) x y(n) m x(z) y(z) R1 R2

6 Differentiation in Z-Domain n x (n)m -z d/dz (x(z)) R1

7 Scaling in Z-Domain an

x(n) m x(z/a) R1/a

8 Initial value theorem x(0) = Lim x(n) = Lim x(z) -

9Final value theorem x(g) = Lim x(n) =Lim (z-1) x(z)

-

PROPERTIES OF ROC FOR Z TRANSFORM: The ROC of x(z) consists of a ring in the z place centered about the origin. The ROC does not contain any poles. If x(n) is of finite duration, then the ROC is the entire z plane, except possibly z=0

and / or z = w

If x(n) is a right sided sequence, and if the circle |z| = r0 is the ROC, then all finitevalues of z for which |z| > r0 will also be in the ROC.

If x(n) is a left sided sequence, and if the circle |z| = r0 is the ROC, then all thevalues of z for which 0 < |z|


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If x(z) is rational and if x(n) is left sided, the ROC is the region inside the innermost non-zero pole.

FILTERS

NEED OF FILTERS IN DIGITAL SIGNAL PROCESSING:

Filtering is used in digital signal processing in a variety of ways. For example,

removal of undesirable noise from desired signals, spectral shaping such as equalization

of communications channels and for performing spectral analysis of signals and so on.

DEFINITION: To process signals we have to design and implement systems called

filters.

TYPES OF FILTERS:

Filters

COMPARISON BETWEEN DIGITAL & ANALOG FILTERS:

DIGITAL FILTER ANALOG FILTER

1 Operates on digital samples of the signal Operates on analog signal

2 It is governed by linear difference equations It is governed by linear

differential equations

3 It consists of adders, multipliers and delay

implemented in digital logic hard ware or software

It consist of electrical

components like resistors,

capacitors and inductors

4 In digital filters, the filter coefficient are designed to

satisfy the desired frequency response

In analog filters the

approximation problem is

solved to satisfy the desired

frequency response

Analog filters Digital Filters

FIR IIR

(Finite Duration

Impulse Response)

(Infinite Duration

Impulse Response)


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DESIRED DIGITAL FILTER:

In digital signal processing there are two types of systems. The first type of

system perform signal filtering in the time domain and hence are called digital filters.

The second type of systems provide signal representation in frequency domain and are

called spectrum analyzers.

ADVANTAGE OF DIGITAL FILTERS:

High thermal stability due to absence of resistors, inductors and capacitors. The performance characteristics like accuracy, dynamic, range, stability and

tolerance can be enhanced by increasing length of the resistors.

The digital filters are programmable. Multiplexing and adaptive filtering are possible.

DISADVANTAGE OF DIGITAL FILTERS:

The bandwidth of discrete signal is limited by the sampling frequency. The performance of the digital filter depends on the hardware used to implement

the filter

COMPARISON BETWEEN FIR AND IIR:

FIR IIR

1 All the infinite samples of impulse

response are considered

Only N samples of impulse response are

considered

2 The impulse response cannot be directly

converted to digital filter transfer

function

The impulse response can be directly

converted to digital filter transfer function

3 The specifications include the desired

characteristics for magnitude response

only

The specifications include the desired

characteristics for both magnitude and

phase response

ADVANTAGES AND APPLICATIONS OF DSP

Design a

proto type

low pass

filter of

order N

Perform

analog to

analog

transformati

on

Digitize the

resultant

analog filter

Desired

digital

filter

fig: BLOCK DIAGRAM FOR DESIRED DIGITAL FILTER


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ADVANTAGES OF DSP:

FLEXIBILITY: Digital programmable systems allow flexibility in reconfiguringthe DSP operations by simply changing the program.

ACCURACY: DSP provides better control of accuracy requirements whiletolerance limits has to be met in the analog counterpart.

EASY STORAGE: Digital signals can be easily stored in magnitude mediawithout deterioration or loss of signal fidelity. They can also be easily transported

and processed off time in remote laboratories.

PROCESSING: DSP allows for the implementation of more sophisticated signalprocessors than its analog counterparts.

LIMITATIONS OF DSP:

The conversion speed of ADC and the processing speed of signal processors

should be very high to perform real time processing signals of high bandwidth

requires easy sampling rate ADC s and Fast processors.

APPLICATIONS OF DSP:

Speech processing; Speech compression and decompression for voice storagesystem and for transmission and reception of voice signals.

Human voice is Text digitally. This is less sensitive to cross talk and noise.Reason: Coding is used.

In Analysis of Seismic waves. Earthquakes and volcanic explosives since analoganalysis takes more time.

In detection of underground objectives like submarines. In RADAR for detection of distance object. In Bio-medical applications. Used in electronic music synthesizers. In Boolean market to estimate next days sensex. In design of FIR and IIR filters.

INTRODUCTION TO DIGITAL IMAGE PROCESSING

In general, any two-dimensional function that bears information can be

considered an image. Multi dimensional signal processing is only one of many advanced

and specialized topics is signal processing. The term digital image processing generally

refers to processing of a two-dimensional picture by digital computers. A digital image is

an array of real or complex no represented by a finite no. of bits. An image given is the


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form of a transparency; slide, photograph or chat is first digitized and stored as a matrix

of binary digits in computer memory.

This digitized image can then be processed and/or displayed on a high-

resolution television monitor. For display, the image is stored in a rapid access buffer

memory, which refreshes the monitor at 30 frames/second to produce a visibly continuous

display. Program input to the computer are made through a terminal, and the outputs are

available, on a terminal, television monitor, or printer/plotter. The fundamentals

requirement of digital processing is that images be sampled and quantized. The sampling

rate (no. of pixels per unit area) has to be large enough to preserve the useful information

in an image. It is determined by the bandwidth of the image.

METHODS OF DIGITAL IMAGE PROCESSING:

IMAGE REPRESENTATION AND MODELING: -In image representation one is concerned with characterization of the quantity

that each picture element represents. Image models give a logical or quantitative

description of the properties of this function. An important consideration image in the

fidelity or intelligibility criteria for measuring the quality of an image or the

performance of processing technique knowledge. Fidelity criterion helps in designing

the imaging sensor, because it describes us the variables that should be measured most

accurately

IMAGE ENHANCEMENT: -In image enhancement, the goal is to accentuate certain image features for

subsequent analysis or for image display. Image enhancement is useful in features

extraction, image analysis and visual information display. The enhancement process it

self does not increase the inherent information content in the data. It simply

On

line

buffer

Displa

y

Record

Digi

tal

Storage

Digital

Comput

er

Imaging

System

Sample

&

quantizeObject

Output

Refresh/

Store

fig: DIGITAL IMAGE PROCESSING SEQUENCE


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emphasizes certain specified image characteristics. Enhancement algorithms are

generally interactive and application dependent.

IMAGE RESTORATION:Image restoration refers to removal or minimization of known degradations in

an image. The image of a point source is blurred and degraded due to noise by an

imaging system. A fundamental result in filtering theory is used commonly for image

restoration is called the Wiener filter.

IMAGE ANALYSIS: -Image analysis is concerned with making quantitative measurements from an

image to produce a description of it more advanced image analysis system measure

qualitative information and use it to make a sophisticated decision, such as controlling

the arm of a robot to move as object after identifying it.

IMAGE DATA COMPRESSION: -Typical television images generate data rates exceeding 10 million bytes per

second. These are other image sources that generate even higher data rates storage

and/or transmission of such data require large capacity and/or bandwidth, which could

be very expensive. Image data compression techniques are concerned with reduction

of the number of bits required to store or transmit images with out any appreciable

loss of information.

TWO DIMENSIONAL FOURIER TRANSFORM

Two-dimensional Fourier transform are of fundamental importance in digital image

processing it is given by

F(P1, P2) = f(x,y)exp[-j2T(xP1+yP2)] dx dy

TWO DIMENSIONAL Z TRANSFORM

A useful generalization of Fourier transform is the z transforms which for a two

dimensional complex sequence x(m,n) is defined as

X(z1, z2) = x(m,n) z1-m

z2-n

Where z1, z2, are complex variable. The set of values of z1 and z2 for which this series

converges uniformly is called the region of convergence. The z transform of the impulse

response of a linear shift invariant discrete system is called its transfer function. Applying

convolution theorem for z transforms

- -

m =-w =-


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Y(z1, z2) = H (z1, z2) X(z1, z2)

H(z1, z2) = Y(z1, z2)/X(z1, z2)

i.e., the transfer function is also the ratio of the z transforms of the output and the input

sequences.

APPLICATIONS OF DIGITAL IMAGE PROCESSING

Digital image processing has a broad spectrum of application such as remotesensing via satellites and other space crafts, image transmission and storage for

business applications, radar, sonar and acoustic image processing robotics and

automated inspection of industrial parts images acquired by satellites are useful in

tracking of earth resources, geo-graphical mapping, prediction of agricultural

crops, urban growth and weather.

In medical applications one is concerned with processing of chest x-rays,cineangiograms, projection images of trans axial topography and other medial

images that occur in radiology and ultrasonic scanning.

BIBLIOGRAPHY

1. Digital Signal Processing OPPENHEIM AND SCHAFER2. Discrete time Signal Processing OPPENHEIM AND SCHAFER3. Digital Signal processing Using MATLAB VINAY K. INGLE & JOHN G. PROAKIS4. Theory and applications of DSP RABINER GOLD5. Digital Signal Processing B. RAMACHANDRAN6. Digital Signal Processing P. RAMESH BABU7. Digital Signal Processing A. NAGOOR KANI8. Fundamentals of Digital Image Processing A.K. JAIN

29883125 digital signal processing

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