Signals (kỹ THUẬT TRUYỀN số LIỆU SLIDE)

Outline  Analog and digital data/signals  Time and frequency domain views of signals  Bandwidth and bit rate  Transmitting digital signals as analog  Theoretical data rate  Signal

Physical Layer:

Data and Signals

Outline

 Analog and digital data/signals

 Time and frequency domain views of

signals

 Bandwidth and bit rate

 Transmitting digital signals as analog

 Theoretical data rate

 Signal impairment

Analog vs Digital Data

 Data take on continuous values

 E.g., human voice, temperature reading

 Data take on discrete values

 E.g., text, integers

Periodic Signals

 A signal x(t) is periodic if and only if

x(t) = x(t+T) -  < t < 

value

time

period

 General form: x(t) = A×sin(2 ft +  )

period

T = 1/f

peak amplitude

0 0.5 1 1.5 2 2.5 3

A = 1, f = 1,  = /4

Varying Sine Waves

0 0.5 1 1.5 2 2.5 3 -1.5

-1 -0.5 0 0.5 1 1.5

0 0.5 1 1.5 2 2.5 3

Demo: sine.py

) 3 2

sin(

3

1 )

2 sin(

)

signal strength

frequency

Time Domain Representation

 plots amplitude as a function

of time

Frequency Domain Representation

 plots each sine wave’s peak amplitude against its frequency

Demo: Equalizer

Fourier Analysis

 Any periodic signal can be represented

as a sum of sinusoids

 known as a Fourier Series

 E.g., a square wave:

=

Joseph Fourier (1768-1830)

rd harmonic 5 th harmonic

…

0 cos( 2 ) sin( 2 ) )

c t

j

n e c t

x( ) 2  0

The time and frequency domains of a nonperiodic signal

Frequency Spectrum

signal

0 0 f0 3f0 5f0 7f0 9f0 11f0

Bandwidth

 A property of a medium

 Indicates the difference between the highest

and the lowest frequencies allowed to pass

 <highest freq allowed> – <lowest freq

allowed>

 Also a property of a single spectrum

Cutoff frequency (half of power is lost)

Cutoff frequency (half of power is lost)

Example

4000 to 7000 Hz Can the above

signal pass through?

) 6000

sin(

3

1 )

2000 sin(

2 )

Digital Signals

 Bit rate – number of bits per second

 Bit interval – duration of 1 bit

time amplitude

bit interval

Two digital signals: one with two signal levels and the other

with four signal levels

The time and frequency domains of periodic and nonperiodic

digital signals

Baseband transmission

 Sending a digital signal over a channel

without changing it to an analog signal

A digital signal is a composite analog

signal with an infinite bandwidth.

Note

Baseband transmission using a dedicated medium

f = 0 Analog

Digital vs Analog

 Adding 3rd harmonic to improve quality

32

Modulation of a digital signal for transmission on a bandpass channel

Signal Attenuation

 Signal strength falls off with distance

of frequency

Transmission medium

Sometimes the decibel is used to measure signal power

in milliwatts In this case, it is referred to as dBm and is calculated as dB m = 10 log10 P m , where P m is the power

in milliwatts Calculate the power of a signal with dBm =

−30.

Solution

We can calculate the power in the signal as

Example

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

Example

Signal Distortion

 Distortion  Change in signal shape

 Only happens in guided media

 Propagation velocity varies with frequency

Noise

between the transmitter and the

Bit Rate = 2 × Bandwidth × log2L

Bit Rate = 2 × Bandwidth × log2L

Harry Nyquist (1889-1976)

We need to send 265 kbps over a noiseless channel with

a bandwidth of 20 kHz How many signal levels do we need?

A telephone line normally has a bandwidth of 3000 The

signal-to-noise ratio is usually 3162 Calculate the

theoretical highest bit rate of a regular telephone line.

Example

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.

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, use the Shannon capacity

followed by the Nyquist formula

Example

The Shannon capacity gives us the

upper limit; the Nyquist formula tells us

how many signal levels we need.

Note

 Time it takes for an entire message to

completely arrive at the destination

time

propagation

time

First bit arrives

Last bit arrives

Sender Receiver

Propagation time

Transmission time

Bandwidth-Delay Product

 Cross section = bandwidth

 Length = delay

number of bits that can fill the link

Figure Filling the link with bits for case 1

Summary

be transmitted

signal allows easier analysis

 Fourier analysis

frequencies to pass

distortion, and noise