SignalsAnalog and DigitalAnalog and Digital Data & SignalsPeriodic & Aperiodic Signals

Contents

Information can be voice, image, numeric data, characters or any message that is readable and has meaning to the destination

Generally, the information is not in a form that can be transmitted over a Link

The binary digits must be converted into a form that Transmission Medium can accept

The data stream of 1s and 0s must be turned into Signals

Signals

ANALOG◦Refers to something that is Continuous

CONTINUOUS◦ A set of specific points of data and all possible points between them

Analog

DIGITAL◦Refers to something that is Discrete

DISCRETE◦ A set of specific points of data with no points in between

Digital

Analog Data◦Human Voice◦Analog Clock

Digital Data◦Data stored in the memory of a computer

◦Digital Clock

Analog and Digital Data

It is a continuous waveform that changes smoothly over time

As the wave moves from value ‘ A’ to value ‘B’, it passes through and includes an infinite number of values along its path

A digital signal is discrete. It can have only a limited number of defined values, often as simple as 1s and 0s

The transition of a digital signal from value to value is instantaneous like a light being switched ON and OFF

ANALOG & DIGITAL Signal

Analog and Digital Signals

Periodic and Aperiodic Signals

Periodic

Signals(Analog or Digital)

Aperiodic

A signal is called Periodic if it completes a pattern within a

measurable time frame called a Period and then repeats that

pattern over identical subsequent Periods.

The completion of one full period is called a cycle.

Periodic Signals

Periodic Signal Example

An Aperiodic or Non-Periodic signal is the one that changes constantly without exhibiting a pattern or cycle that repeats

over time

Aperiodic Signals

Aperiodic Signals

Analog signals can be classified into:

◦Simple Analog Signal (Sine wave)

◦Composite Analog Signal

Analog Signals

Simple Analog Signal(Sine Wave)

Sine waves can be fully described:

◦Amplitude◦Period / Frequency◦Phase

Simple Analog Signal(Sine Wave)

Amplitude of a signal is the value of the signal at any point on the wave

It is equal to the vertical distance from a given point on the wave form to the horizontal axis

The maximum amplitude of the sine wave is equal to the highest value it reaches on the vertical axis

Amplitude measured in Volts, Amperes or Watts

Amplitude

Amplitude

Period: Amount of time ( in seconds) a signal need to complete one cycle

Frequency: Number of cycles completed in one second

Unit of Period: Period is expressed in seconds

Period & Frequency

Period and Frequency

T= 1 / f OR f=1 / T

Seconds____HertzMilliseconds____Kilohertz

Microseconds____MegahertzNanoseconds____GigahertzPicoseconds____Terahertz

Units of Period & Frequency

Example

A Sine wave has a frequency of 6 Hz. What is its period?

Solution

sec17.06

11

fT

Example

A Sine wave completes one cycle in 4 seconds. What is its frequency?

Solution:Hz

Tf 25.0

4

11

Another Way to Look at Frequency

Measurement of the rate of change

How fast the wave moves from its lowest to its highest point

A 40 Hz signal has half the frequency of a 80 Hz signal, therefore each cycle takes twice as long to complete one cycle

Changes in Short Time: High Frequency

Two Frequency Extremes

No change at all Zero frequency

Instantaneous changes Infinite frequency

Change in a short span of time means high frequency.

Change over a long span of time means low frequency.

Phase

Phase describes the position of the waveform relative to time zero

Phase describes the amount of backward or forward shift of the waveform

Measured in Degrees or Radians

It indicates the status of the first cycle

Phase is measured in Degrees or Radians

360 degrees – 2 pi RadiansA phase shift of 360 degrees correspond to a shift of a complete period

Phase

Phase

Example 4.7

A sine wave is offset of a cycle with respect to time zero. What is its phase?

6

1

Wavelength binds the period or the frequency of a simple sine wave to the propagation speed of medium

Frequency of signal is independent of the medium, while the wave length depends on both frequency and medium

Wavelength is the distance a simple signal can travel in one period

Wavelength = propagation speed * Period

Wavelength

Wavelength

Control of Signals

Signal can be controlled by three attributes:

◦Amplitude◦Frequency◦Phase

Control of Signals- Amplitude

Control of Signals- Frequency

Control of Signals- Phase

Time Domain plots show changes in signal amplitude w.r.t Time

It is an Amplitude versus Time Plot Phase and Frequency are not explicitly

measured on a Time domain plot To show the relationship between amplitude

and Frequency, we can use what is called a Frequency Domain Plot

Time and Frequency Domain

Time and Frequency Domain

Time and Frequency Domain Example

Second type of Analog Signals, that is composed of multiple sine waves

So far we have been focused on simple periodic signals or sine waves

Many useful sine waves do not change in a single smooth curve b/w minimum and a maximum amplitude.

They jump, slide , wobble and spikeAs long as as any irregularities are consistent, cycle after cycle, a signal is still Periodic

It can be shown that any periodic signal no matter how complex can be decomposed into a collection of sine waves, each having a measurable amplitude, frequency & phase

We need FOURIER ANALYSIS to decompose a composite signal into its components

Composite Signals