SIGNALS AND SYSTEMS

EEE F243 / INSTR F243

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Lecture 01

Introduction to Signals

Todays Session

Signals

Size of a Signal

Classification of Signals

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Classification of Signals

Useful Signal Operations

Signal

Signal:

Signal is a physical quantity which varies with time, space,

frequency etc.

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Examples: Electricity, Voice, Photons, Telephonic conversation, TV

signal etc.

Signal should be a function of an independent variable mainly time.

Though others may be space, frequency etc.

Size of a Signal

Signal Energy:

It takes account of both amplitude and duration.

= dttfE 2|)(|

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V2s (A2s)

Signal Power:

Time average of the signal energy is the signal power.

V2 (A2)

= dttfE f2|)(|

=2/

2/

2)(

1lim

T

TTf dttf

TP

Energy Signal: If and only if it has finite energy and zero

average power.

Power Signal: If and only if its power is finite and energy is

infinite.

Size of a Signal

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Generally all periodic signals are power signals.

A signal may not get classified as an energy or power signal, if it does

not satisfy both the criteria. It is then called as neither energy nor

power signal. Example: Ramp signal f(t) = t

It increases indefinitely as t

Examples

Find the energies of the following signals:

0

1

t

f(t) = sin t 1

0 t1

f(t) = t

2

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-2

2

8

-8

f(t) = t3

Find the power of the following signal:

12

Signal

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Classification

Signal Classification

Continuous Time / Discrete Time Signals:

- Uniquely defined at all times / Defined at discrete intervals of time.

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Signal Classification

Analog Signals Amplitude can take any value in continuous range.

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Digital Signals Amplitude can take only finite number of values.

Signal Classification

Periodic Signal: Repeats after finite intervals.

for all t

Smallest value of T satisfies above equation Period.

)()( Ttftf +=

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Aperiodic Signal: Does not repeat after regular intervals.

for all t

A periodic signal can be generated by its periodic extension.

A periodic signal remains unchanged when time shifted by one

period.

)()( Ttftf +

Signal Classification

Example of Periodic Signals:

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Tt

Signal Classification

Example of Aperiodic Signals:

2

f1(t)

2

f1(t)

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1

0

0

f2(t)

t

t

1

0

0

f2(t)

t

t

Signal Classification

Causal Signal: A signal which does not start before t =0.

0)( =tf 0

Signal Classification

Deterministic Signal:

A signal whose description is known completely either by

mathematically or by graphically.

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Random Signal:

A signal which can only be predicted by probabilistic description.

Signal

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Operations

Signal Operations

Shifting: shifting of a signal certain time.

)()( tfTt =+

)()( Ttft =

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Signal Operations

Scaling: The compression or expansion of a signal by time.

Compression: )()( atft =

1>a

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Expansion:

=a

tft)(

1>a

f(t/2)

f(2t)

Signal Operations

Inversion (Reversal): Inverting or folding a signal.

)()( tft =)()( tft =

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Combined Operations

One operation for example is:

First way: (1) Time shift:

( )batf

( )btf

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(2) Time scaling:

Second way: (1) Time scaling:

(2) Time shift:

( )batf

( )atf

( )batfa

btaf =

Examples

Express following signals f2(t) and f3(t) in terms of f(t):

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f3(t)

Examples

For the following signal f(t): find (i) f(-t) (ii) f(t+6) (c) f(t/2)

0.5

f(t)

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t0

0.5

-1

6

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