SIGNALS AND SYSTEMSLECTURE NOTE #1

Presentation by:I.NelsonSL/ECE

SSN College of Engineering

www.EEENotes.in

Objective• What is a signal?• What is a system?• How signal and system can be classified?• How signal can be generated using basic

building blocks?• How signals and systems are analyzed• Conversion of analog signal into discrete

signal• Realization of digital systems

www.EEENotes.in

What is a signal?

• An observed data representing a physical phenomenon is called a signal.

• The signal is a continuously varying phenomenon which represented as a function of time.

signal = function x(t), Rt ∈

www.EEENotes.in

Signal represents Change

Definition:

“ Any physical quantity that varies with time is called signal”

www.EEENotes.in

An electrical signal

* One dimensional signal

V(t)

www.EEENotes.in

Multidimensional signal

An ordered set of one-dimensional signalsV(t)=[v1(t) ,v2(t), v3(t), …,vN(t)]

It is the set of voltages existing at the terminals of a multiport.

v3(t)

v2(t)

v1(t)

v6(t)

v4(t)

v5(t)

www.EEENotes.in

Examples

• Audio signal:

0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0 1 0 0 0 0 1 2 0 0 0 1 4 0 0 0- 0 . 2 5

- 0 . 2

- 0 . 1 5

- 0 . 1

- 0 . 0 5

0

0 . 0 5

0 . 1

0 . 1 5

0 . 2

0 . 2 5

Amplitude

Time (ms)

www.EEENotes.in

Video Signal

www.EEENotes.in

BIOMEDICAL SIGNALS

EEG Signal

www.EEENotes.in

Image Signalwww.EEENotes.in

CLASSIFICATION OF SIGNALSThe signal are classified as

1. Continuous and Discrete time 2. Analog and Digital3. Even and Odd4. Periodic and Aperiodic5. Deterministic and Random6. Energy and power

www.EEENotes.in

Classification of signals

1. Continuous time and discrete time signals

* A signal x(t) is said to be a continuous time signal if it is defined for all time t.

* Continuous time signal arises when a physical waveform is converted to electrical signal

www.EEENotes.in

Classification of Signals ( Continued)

• Continuous time signals

• Example – Voltage, current, pressure , temperature, velocity etc.

www.EEENotes.in

Classification of signals( Continued)

• Discrete time signals – It is defined only at discrete instants of time.

• A discrete time signal is derived from a continuous time signal by sampling it at a uniform rate.

• A DT signal is mathematically represented as

x[n] Where n is time index, which always an integer (i.e.) n=0,1,,2,3,4,…….

www.EEENotes.in

Discrete Time signal

1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

6

7

8

9

10

X[n]

n

X[2]

X[7]

www.EEENotes.in

• Discrete time signals

Examples of discrete time signals in nature:

• DNA base sequence• Population of nth generation of

certain species

www.EEENotes.in

Analog Signal

• The amplitude of the signal is defined for all the value of time.

eg. All continuous time signals

www.EEENotes.in

Digital signal

• The amplitude and time are quantized i.e., it takes only fixed values.

• But for discrete time signal only time is quantized.

www.EEENotes.in

Classification of signals( Continued)

Even and Odd SignalEven Signal A CT signal x(t) is said to be an even signal if it satisfies the

condition. x(-t) = x(t) for all t

x(t)

t

A

Even signals are symmetric about time origin

www.EEENotes.in

Odd Signal The signal x(t) is said to be an odd signal if it satifies the

condition x(-t) = - x(t) for all t

Odd signals are anti-symmetric about time origin

x(t)

t

-A

A

www.EEENotes.in

Any CT signal x(t) is expressed as

x(t) =xe(t) + xo(t)

Where xe(t) is the Even component and xo(t) is the Odd component of the signal x(t).

( ))()(

21)( txtxtxe −+=

( ))()(21)( txtxtxo −−=

www.EEENotes.in

Classification of signals( Continued)

Periodic and nonperiodic SignalsA periodic signal x(t) is a function that

satisfies the condition x(t) = x(t +T) for all t.

eg. Sinusoids,Square wave, sawtooth and etc.,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time

Am

plitude

Sinusoidal Signal

www.EEENotes.in

The smallest value of T that satisfies the above condition is called fundamental period

Fundamental freq f= 1/TAny signal for which there is no value

of T to satisfy the condition is called aperiodic Signal

www.EEENotes.in

Discrete Periodic signal

A signal is discrete periodic if it satisfies the relation

x[n]=x[n+N]

where N is the period of the signal.

0 5 1 0 1 5 2 0 2 5 3 0 3 5- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

x[n]

n

www.EEENotes.in

Classification of signals( Continued)

Deterministic and random signalsA deterministic signal is a signal about

which there is no uncertainty with respect to its value at any time.

Example of deterministic Signal

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

time

Am

plitude

Sinusoidal Signal

www.EEENotes.in

Classification of signals( Continued) Random signal is a signal about which

there is uncertainty before its actual occurrence.

Eg. Noise generated in an amplifier

www.EEENotes.in

Energy signal and Power signalIn electrical system, a signal can be

represented as a voltage or currentConsider a voltage v(t) developed across

R producing a current i(t).The instantaneous power dissipated in the

resistor is given by p(t) = v2(t)/ROr p(t)= i2(t)/RFor R=1 ohm , whether x(t) is voltage or

current , p(t)=x2(t).

www.EEENotes.in

the total energy of a continuous time signal x(t) as

For Discrete time signal x[n]

∑∞

−∞=

=n

nxE 2][

∫∞

∞−= dt)( 2txE

www.EEENotes.in

Classification of signals( Continued)The average power is given by

The average power of a periodic signal is given by

dttxT

TT TP )(lim

2/

2/

21∫

−∞→=

dttxT

TTP )(

2/

2/

21∫

−

=

www.EEENotes.in

The Average Power of a discrete time signal is

For a Periodic Discrete time signal,

21

0][1P ∑=

−

=

N

nnx

N

2][

121

limN

P ∑+∞→

=−=

N

Nnnx

N

www.EEENotes.in

Classification of signals( Continued)

The signal is referred to as an energy signal if and only if

0< E < ∞The signal is referred to as an power signal

if and only if 0< P < ∞ In particular an energy signal has zero

average power whereas power signal has infinite energy.

www.EEENotes.in

Test your understanding

1. Consider the pair of signal shown . Which one of these two signals is even and which one is odd?

Fig a Fig b

X1(t) X2(t)

www.EEENotes.in

Test your understanding

1. Ans : Fig a – even ,Fig b – odd2. What is the fundamental frequency

of the wave shown below?

Am

plit

ude

0 0.1 0.2 0.3 0.4

Fig : c

www.EEENotes.in

Test your understanding

2. Ans : Fundamental Period = 0.2

3. What is the average power of a triangular wave shown in fig: c?

Ans : 1/3

www.EEENotes.in

SummaryA continuous time signal is defined for

all values of timeDiscrete time signal is defined only at

discrete instants of timeEven signals are symmetric about time

origin but odd signals are antisymmetric about time origin

A periodic signal is one which repeats itself after a particular instant of time.

www.EEENotes.in

Summary ( Continued)

A deterministic signal is one in which there is no uncertainty with respect to its value at any time

A random signal is a signal about which there is uncertainty before its actual occurrence.

An energy signal has zero average power whereas a power signal has infinite energy.

www.EEENotes.in