dsp part 01

Digital Signal ProcessingCSE 4107References:•Digital Signal ProcessingBy, S Salivahanan, A Vallavaraj, C Gnanapriya•Digital Signal Processing

By, John G. Proakis, Dimitris G. Manolakis•Digital Signal Processing

By, Sanjit K. Mitra

G.M.Mashrur-E-Elahi, Lecturer, Dept of CSE, KUET, Khulna-9203

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Syllabus:Discrete time description of signals and system; Fourier transformation of discrete time signals;Discrete Fourier transformation;DSP hardware and software development aids,

Digital Hearing aids; Z-transform. And To be continued…………..


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Signals:Can be a function of time, distance, position,

temperature, pressure etc.Represents some variable of interest

associated with a system.Voltage and current are signals for electrical

system. Force, speed, torque, etc are signals for

mechanical system. Also speech, music, video are signals used in daily life.

Any physical quantity that varies with time, space, or any other independent variable or variables.


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Signal Processing:Method of extracting information from the signal.Depends on the type and nature of the signal.Carrying out algorithmic operations on the signal.

System:Physical device that performs an operation

on a signal.Process the signal for extracting information.Composed of diverse, interacting structures

to perform a desired task.


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Classification of Signals:Depends on the nature of the independent

variables and the value of the function defining the signal.

Classified based on their nature and characteristics in the time domain.

Mainly classified as:◦ Continuous-time signal and◦ Discrete-time signal


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Continuous-time signal:Mathematically a continuous function and

defined continuously in the time domain.


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Discrete-time signal:Specified only at certain time instants.

The amplitude of the signal between two time instant is not defined.

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Classification of Signals:

Both continuous and discrete-time signals are further classified as◦ Deterministic and non-deterministic signals◦ Periodic and aperiodic signals◦ Even and odd signals, and ◦ Energy and power signals



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Deterministic and non-deterministic signals:Deterministic signals:

◦ Functions that are completely specified in time.

◦ Nature and amplitude at any time can be predicted.

◦ Pattern of the signal is regular◦ Examples:

Ramp signal Sinusoidal signal Discrete-time signal


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Deterministic and non-deterministic signals:Non-deterministic signals:

◦ Nature and amplitude at any time can not be predicted.

◦ Probabilistic in nature and can be analyzed only stochastically.

◦ Pattern is quite irregular.◦ Examples:

Thermal noise of an electrical circuit. Number of accident in an year (for understand).

◦ that is why it is called random signal.


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Periodic and aperiodic signals:Periodic signals:

◦ A signal is said to be periodic if it exhibits periodicity.

◦ Has a definite pattern that repeats over and over with a defined fixed repetition period.


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Periodic and aperiodic signals:Periodic signals:

◦ Continuous-time periodic signal is generally expressed as:

◦ Discrete-time periodic signal is generally expressed as:

◦ A fundamental signal is periodic if the period (T0 or N0) is ratio of two integers.

◦ The sum of two periodic signals is periodic signal if the fundamental periods ratio can be represent as ratio of two integers.


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Periodic and aperiodic signals:Aperiodic signals:

◦ A signal is said to be aperiodic if it exhibits no periodicity.

◦ Has no definite pattern that repeats over and over with a defined fixed repetition period.

◦ The sum of two continuous-time periodic signals can be an aperiodic signal also, but not the discrete-time periodic signals.


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Even and Odd signals:Even signals:

◦ Exhibits symmetry in the time domain.◦ Must be identical to its reflection about the

origin.◦ Satisfies:

for a continuous-time signal for a discrete-time signal

◦ Example: produce even signal


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Even and Odd signals:Odd signals:

◦ Exhibits anti-symmetry in the time domain.◦ Not identical to its reflection about the

origin, but to its negative◦ Satisfies:

for a continuous-time signal for a discrete-time signal

◦ Example: produce odd signal


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Energy and Power signals:Energy signals:

◦ Has finite energy and zero average power.◦ is an energy signal if

where E is energy and P is power. ◦ If the condition is false, then the signal is

not the energy signal.


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Energy and Power signals:Power signals:

◦ Has finite average power and infinite energy.

◦ is an energy signal ifwhere E is energy and P is power.

◦ If the condition is false, then the signal is not the power signal.


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Singularity Functions:Are important classification of non-periodic

signals.Used to represent more complicated signals.Examples are:

◦ Unit-impulse function◦ Unit-step function◦ Unit-ramp function and◦ Unit-pulse function (obtained from unit-step signal)


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Unit-impulse Function:The function is defined as:

And

Very useful in continuous-time system analysis.

For discrete-time domain it is called unit-sample signal and defined as:


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Unit-step Function: Integral of unit-impulse function and defined

as:

For discrete-time domain, unit-step signal is defined as:


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Unit-ramp Function:Obtained by integrating the unit-impulse signal

twice or integrating the unit-step function once

Unit-pulse Function:Obtained from the unit-step signals as shown

below:


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Properties of unit-impulse signalSee from book:Digital Signal Processing

By, S Salivahanan, A Vallavaraj, C Gnanapriya


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Representation of Signals: If a signal is represented as byWhere a is a scaling factor and b/a is pure shift

version in the time domain◦ If b/a is positive, then the signal x(t) is shifted to left◦ If b/a is negative, then the signal x(t) is shifted to right◦ If a is positive, then the signal x(t) will have positive

slope◦ If a is negative, then the signal x(t) will have negative

slope◦ If a is less than 0, then x(t) is reflected through the

origin◦ |a|<1 , then x(t) is expanded, else x(t) is compressed

See Examples from books


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Classification of Systems:Broadly classified as:

◦ Continuous-time system The associated signals are continuous (i.e, input,

output)◦ Discrete-time system

The associated signals are discrete (i.e, input, output)

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Classification of Systems:

Both continuous and discrete-time systems are further classified as◦ Static and dynamic systems◦ Linear and non-linear systems◦ Time-variant and time-invariant systems ◦ Causal and non-causal systems, and◦ Stable and unstable systems



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Static and dynamic systems:Static systems:

◦ The output at any specific time depends on the input of that particular time.

◦ Does not depends on the past or future values of the input.

◦ A system with no memory or energy storage elements

◦ Examples: Simple resistive network


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Static and dynamic systems:Dynamic systems:

◦ The output at any specific time depends on the input of that specific time and at other time.

◦ A system with memory or energy storage elements

◦ Characterize by differential equation for continuous-time system or a difference equation for discrete-time system

◦ Examples: Electrical circuit consisting of a capacitor or an

inductor


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Linear and non-linear systems:◦ Linear system is one in which superposition

principle holds◦ A system with two inputs and , the

superposition is defined as:

Where a1 and a2 are weights added to the inputs and is the response.

◦ Thus, if a system’s response to the sum of weighted inputs is same as sum of the weighted response, then the system is linear.

◦ Otherwise the system is non-linear.◦ Does the system described by the differential

equation is linear?


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Time-variant and time-invariant systems:

◦ The system in which the input-output relationship does not vay with time, called time-invariant system. Also called fixed system.

◦ The condition for a system to be fixed is:

◦ Otherwise the system is time-variant◦ The systems satisfying both linearity and

time-invariant conditions are called linear, time-invariant (LTI) system.


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Causal and non-causal systems:Causal systems:

◦ Response to an input does not depends on the future values of that input.

◦ Depends only on the present and/or past values of the input.

◦ Called non-anticipatory.◦ Some examples (equations):


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Causal and non-causal systems:Non-causal systems:

◦ Response to an input depends on the future values of that input.

◦ Are unrealisable.◦ Called anticipatory.◦ Some examples (equations):


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Stable and Unstable systems:

◦Self study


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Simple manipulation of discrete-time signals:

◦ In signal processing, the signal undergoes manny manipulations involving independent and dependent variables.

◦ Some of these manipulations are: Shifting the signal in the time domain Folding the signal and Scaling the signal in the time domain


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Available at:

◦ http://sites.google.com/site/mashrurelahi/home/digital-signal-processing

◦ Thanks to all for now!!!!

http://sites.google.com/site/mashrurelahi/home/digital-signal-processing



dsp part 01

Documents

y periodic signals

y continuoustime signal

y aperiodic signals

discretetime signals

y energy signals

y odd signals

discretediscretetime

discretetime periodic