data and signals lecture 1

8/3/2019 Data and Signals Lecture 1

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Graduate Program in Telecommunications, GMU TCOM 500 - 20121

Data and Signals

Analog and digital data transmission

Time and frequency domain

Baseband and bandpass transmission

Transmission impairments

Data rate limits

Performance metrics

Forouzan Chapter 3


Introduction

Information: text, numbers, audio, images, video.

The term analog data refers to information that is continuous;

digital data refers to information that has discrete states.

Analog data take on continuous values. Digital data take on

discrete values.

To be transmitted, data must be transformed to electromagnetic

signals.


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Central questions for this course:

How is information represented in digital form?

-Where do bits come from?

How is digital information processed and transmitted?

-What is the best way to send digital information to a remote

location?

What are the properties and limitations of transmission media?

How does one make exchange of digital information reliable

and secure?

Introduction


Text: Unicode and ASCII (see appendix A)

In ASCII, 8 bits are used to encode characters that are common in

English text (plus a number of control characters).

Unicode uses 32 bits to represent a symbol or character used in any

language in the world.

Numbers: Decimal to binary conversion.

Audio: Analog to Digital Converters (ADCs) are used to digitize a

speech signal.

Digitizing Information


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Analog and Digital Signals

Like the data they represent, signals can be either analog or

digital.

An analog signal has infinitely many levels of intensity over a

period of time.

A digital signal, on the other hand can have only a limited

number of defined values. Although each value can be any

number, it as often as simple as 1 and 0.


Periodic and Nonperiodic signals

Both analog and digital signals can take one of two forms:

periodic or nonperiodic.

A periodic signal completes a pattern within a measurable time

frame, called a period, and repeats that pattern over subsequent

identical periods.

A nonperiodic signal changes without exhibiting a pattern or

cycle that repeats over time.

In data communications, we commonly use periodic analog

signals and nonperiodic digital signals.


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Periodic analog signals

Periodic analog signals can be classified as simple or composite.

A simple periodic analog signal, a sine wave, cannot be

decomposed into simpler signals.

A composite periodic analog signal is composed of multiple sine

waves.

A sine wave is the most fundamental form of a periodic analog

signal.A sine wave can be represented by three parameters: the peak

amplitude, the frequency, and the phase.



The peak amplitude of a signal is the absolute value of its highest

intensity, proportional to the energy it carries.


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Period refers to the amount of time in seconds. A signal needs to

complete 1 cycle.

Frequency refers to the number of periods in 1 second.Frequency and period are the inverse of each other.

Period is expressed in seconds and frequency is expressed in

Hertz (Hz), which is cycles per second.



Two signals with the same amplitude and phase, but different

frequencies.


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Frequency is the rate of change with respect to time.

Change in a short span of time means high frequency.

Change over a long span of time means low frequency.

If a signal does not change at all, its frequency is zero.

If a signal changes instantaneously, its frequency is infinite.


Periodic signals: phase

The term phase describes the position of the waveform relative to time 0. If we

think of the wave as something that can be shifted backward or forward along

the time axis, phase describes the amount of that shift. It indicates the status of

the first cycle. Phase is measured in radians or degrees


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

While the frequency of a signal is independent of the medium, thewavelength depends on both the frequency and the medium.

Wavelength = propagation speed x period

= propagation speed / frequency

f

c

frequencyf

speednpropagatioc

hwavelengt

The propagation speed of EM signals depends on the medium and

on the frequency of the signal. eg.. c= 3x108 m/s in vacuum and

c 2x108 m/s in data cable.


Time and frequency domains

The time domain plot shows changes in signal amplitude with

respect to time.

Frequency domain plot shows the relationship between peak

amplitude and frequency.


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Why bother with frequency domain?

In many applications, the frequency content of a signal is very

important.

For example, in radio communications signals must be limited

to occupy only a set of frequencies allocated by the FCC.

Hence, understanding and analyzing the spectrum of a signal is

crucial from a regulatory perspective.

Often, features of a signal are much easier to understand in

the frequency domain.

The operation of many systems is much easier to understand in

the frequency domain. Example: A low-pass filter retains low

frequency components of the spectrum and removes high-frequency components.


Composite signals

A single-frequency sine wave is not useful in data

communications; we need to send a composite signal, a signal

made of many simple sine waves.

If the composite signal is periodic, the decomposition gives a

series of signals with discrete frequencies.

If the composite signal is nonperiodic, the decomposition gives a

combination of sine waves with continuous frequencies.


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A Composite periodic signal



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A Composite nonperiodic signal

In time domain representation of this composite signal, there are an

infinite number of simple sine frequencies (frequencies are

continuous).

Although the number of frequencies in human voice is infinite, the

range is limited. A voice signal contains a continuous range of

frequencies between 0 and 4 KHz.


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Signal Bandwidth

The range of frequencies contained in a composite signal is its

bandwidth. It is the difference between the highest and lowest

frequencies contained in that signal.


Signal Bandwidth

An example of a nonperiodic composite signal is the signal

propagated by an AM or FM radio station.

In the United States, each AM radio station is assigned a 10-kHz

bandwidth. The total bandwidth dedicated to AM radio ranges from

530 to 1700 kHz.

Each FM radio station is assigned a 200-kHz bandwidth. The total

bandwidth dedicated to FM radio ranges from 88 to 108 MHz.


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Digital Signals

A digital signal can have two or more levels.

In general, if a signal has L levels, each level represents log2L bits.


Bit rate and bit length

Most digital signals are nonperiodic, and thus frequency and period

are not appropriate characteristics. Bit rate and bit length are used to

describe digital signals instead.

Bit rate is the number of bits sent in 1 second, expresses in bits per

sec (bps).

The bit length is the distance one bit occupies on the transmission

medium.

Bit length = propagation speed x bit duration.


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Bit rate and bit length

Assume we need to download text documents at the rate of 100

pages per minute. A page is an average of 24 lines with 80

characters in each line. If we assume that one character requires 8bits, what is the required bit rate of the channel?

What is the bit rate for high-definition TV (HDTV)?

HDTV uses digital signals to broadcast high quality video signals.

The HDTV screen is normally a ratio of 16 : 9. There are 1920 by

1080 pixels per screen, and the screen is renewed 30 times per

second. Twenty-four bits represents one color pixel.

The TV stations reduce this rate to 20 to 40 Mbps through

compression.


Digital signal as a composite analog signal

Based on Fourier analysis, a digital signal is a composite analog

signal. The bandwidth is infinite.

Fourier analysis can be used to decompose a digital signal.

If the digital signal is periodic, which is rare in digital

communications, the decomposed signal has frequency domain

representation with an infinite bandwidth and discrete frequencies.

If the digital signal is nonperiodic, the decomposed signal still has

an infinite bandwidth, but the frequencies are continuous.


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Digital signal as a composite analog signal

Note that both bandwidths are infinite, but the periodic signal has

discrete frequencies while the nonperiodic signal has continuous

frequencies.


Transmission of digital signals

A digital signal, periodic or nonperiodic, is a composite analog

signal with frequencies between zero and infinity (infinite

bandwidth).

We can transmit a digital signal by using one of two different

approaches: baseband transmission or bandpass transmission (using

modulation).

Baseband transmission means sending a digital signal over achannel without changing the digital signal to an analog signal.


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Baseband transmission

Baseband transmission requires that we have a low-pass channel, a

channel with a bandwidth that starts from zero. This is the case if

we have a dedicated medium with a bandwidth constituting onlyone channel.


Baseband transmission

Baseband transmission of a digital signal that preserves the shape of

the digital signal is possible only if we have a low-pass channel

with an infinite or very wide bandwidth.

Baseband transmission over a low pass channel with wide bandwidth


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Bandpass transmission

If the available channel is a bandpass channel, we cannot send the

digital signal directly to the channel; we need to convert the digital

signal to an analog signal before transmission.


Attenuation means a loss of energy

Transmission Impairments


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The decibel (dB) measures the relative strengths of two signals orone signal at two different points.

The decibel value is negative if the signal is attenuated and

positive if the signal is amplified.

Relative power gain or attenuation in decibels is given by

Ohms Law can be used to transform the power

equations to voltage.

Decibel

1

210log10P

PPdB

1

210log20V

VV

dB

R

VP

2


Suppose a signal travels through a transmission medium and its power is

reduced to one-half. This means that P2 is (1/2)P1. In this case, the attenuation

(loss of power) can be calculated as

A loss of 3 dB (3 dB) is equivalent to losing one-half the power.

A signal travels through an amplifier, and its power is increased 10 times. Thismeans that P2 = 10P1 . In this case, the amplification (gain of power) can be

calculated as

Decibel


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One reason that engineers use the decibel to measure the changes

in the strength of a signal is that decibel numbers can be added (or

subtracted) when we are measuring several points (cascading)instead of just two. In Figure 3.27 a signal travels from point 1 to

point 4. In this case, the decibel value can be calculated as

Decibel


Sometimes the decibel is used to measure signal power in milliwatts. In this

case, it is referred to as dBm and is calculated as dBm = 10 log10 Pm , where

Pm is the power in milliwatts. Calculate the power of a signal with dBm = 30.

Solution

We can calculate the power in the signal as

Decibel


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The loss in a cable is usually defined in decibels per kilometer (dB/km). If the

signal at the beginning of a cable with 0.3 dB/km has a power of 2 mW, what

is the power of the signal at 5 km?

Solution

The loss in the cable in decibels is 5 (0.3) = 1.5 dB. We can calculate the

power as

Decibel


Distortion can occur in a composite signal made of different

frequencies. Different frequency component experience different

transmission delays.

Distortion


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Several types of noise, such as thermal noise, induced noise,

crosstalk, and impulse noise, may corrupt the signal.

Noise


Signal to noise ratio is defined as

Signal to Noise Ratio (SNR)

powernoiseaverage

powersignalaverageSNR SNRlog10SNR 2dB


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The power of a signal is 10 mW and the power of the noise is 1

W; what are the values of SNR and SNRdB ?

Solution

The values of SNR and SNRdB can be calculated as follows:

Signal to Noise Ratio (SNR)


A very important consideration in data communications is how fast

we can send data, in bits per second, over a channel. Data rate

depends on three factors:

1. The bandwidth available

2. The level of the signals we use

3. The quality of the channel (the level of noise)

Data Rate Limits


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For a noiseless channel, the Nyquist bit rate formula defines the

theoretical maximum bit rate

Bitrate = 2 x bandwidth x log2L.

L is the number of signal levels used to represent data.

Increasing the levels of a signal may reduce the reliability of the

system.

Noiseless channel: Nyquist bit rate


We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz.

How many signal levels do we need?

Solution

We can use the Nyquist formula as shown:

Since this result is not a power of 2, we need to either increase the number of

levels or reduce the bit rate. If we have 128 levels, the bit rate is 280 kbps. If we

have 64 levels, the bit rate is 240 kbps.

Noiseless channel: Nyquist bit rate


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In 1944, Claude Shannon introduced a formula, called the Shannon

capacity, to determine the theoretical highest data rate for a noisychannel:

Capacity = bandwidth x log2(1 + SNR).

Capacity is independent of the number of signal levels used.

Noisy channel: Shannon capacity


We can calculate the theoretical highest bit rate of a regular telephone line. A

telephone line normally has a bandwidth of 3000. The signal-to-noise ratio is

usually 3162. For this channel the capacity is calculated as

This means that the highest bit rate for a telephone line is 34.860 kbps. If we

want to send data faster than this, we can either increase the bandwidth of the

line or improve the signal-to-noise ratio.

The signal-to-noise ratio is often given in decibels. Assume that SNRdB = 36

and the channel bandwidth is 2 MHz. The theoretical channel capacity can be

calculated as



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We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63.

What are the appropriate bit rate and signal level?Solution

First, we use the Shannon formula to find the upper limit.

The Shannon formula gives us 6 Mbps, the upper limit. For better performance

we choose something lower, 4 Mbps, for example. Then we use the Nyquist

formula to find the number of signal levels.

The Shannon capacity gives us the upper limit; the Nyquistformula tells us how many signal levels we need.



Bandwidth: In networking, we use the term bandwidth in two

contexts:

The first, bandwidth in hertz, refers to the range of frequencies in a

composite signal or the range of frequencies that a channel can

pass.

The second, bandwidth in bits per second, refers to the speed of bit

transmission in a channel or link.

Throughput: It is a measure of how fast we can actually send data

through a network.

Performance


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The latency or delay defines how long it takes for an entire

message to completely arrive at the destination from the time the

first bit is sent out from the source.

Latency = propagation time + transmission time + queuing

delay + processing delay

Latency


What is the propagation time if the distance between the two points is 12,000

km? Assume the propagation speed to be 2.4 108 m/s in cable.

Solution

We can calculate the propagation time as

The example shows that a bit can go over the Atlantic Ocean in only 50 ms if

there is a direct cable between the source and the destination.

Latency

speednPropagatio

Distancen timePropagatio


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What are the propagation time and the transmission time for a 2.5-kbyte

message (an e-mail) if the bandwidth of the network is 1 Gbps? Assume that the

distance between the sender and the receiver is 12,000 km and that light travels

at 2.4 108 m/s.

Solution

We can calculate the propagation and transmission time as shown :

Note that in this case, because the message is short and the bandwidth is high,

the dominant factor is the propagation time, not the transmission time. The

transmission time can be ignored.

Latency

Bandwidth

sizeMessageon timeTransmissi


What are the propagation time and the transmission time for a 5-Mbyte message

(an image) if the bandwidth of the network is 1 Mbps? Assume that the distance

between the sender and the receiver is 12,000 km and that light travels at 2.4

108 m/s.

Solution

We can calculate the propagation and transmission times as shown:

Note that in this case, because the message is very long and the bandwidth is not

very high, the dominant factor is the transmission time, not the propagation

time. The propagation time can be ignored.

Latency

data and signals lecture 1

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