Signalling

SIGNALLINGChapter 3

Lesson Objectives

Equations

signalin frequency max2 rateSampling

Sampling and digitising 1

Chapter 3.1.1

Signals and noise

Analogue signals are spoilt by noise Digital signals resist effects of noise

analogue signal without noise

analogue signal plus noise

signal recovered from noise loses detail

digital signal without noise

digital signal plus noise

signal accurately regenerated from noise

Signals and NoiseDigital Signals are much less prone to interference and so I theory should produce higher quality signals e.g. Digital TV and Radio

Sampling a signal

original signal

sampling pulses0 or 1 from clock

sampled waveform

original waveformreconstructedfrom samples

The original signal can be exactly reconstructed if the samplingis frequent enough

Sampling 1Instead of storing a whole waveform a signal can be sampled (digitised) at regular intervals. As long as the signal is sampled at a high enough frequency the original signal can be reconstructed

Problems with sampling

Sampling too slowly misses high frequency detail in the original signal

Original signal

Samples taken fromsignal

Samples alone

Signal ‘reconstructed’from samples

Sampling Problems 1If you sample at the wrong frequency then the original signal cannot be reconstructed accurately .

The optimum sampling frequency is:

2x the highest frequency in the original signal

e.g. a music CD need a highest frequency of 20kHz to be stored so music is sampled at 44.1kHz.

Samples takenfrom signal

Sampling too slowly creates spurious low frequencies (aliases)

Original signal

Samples alone

Signal ‘reconstructed’from samples

Problems with sampling

Sampling Problems 2Another problem is that if you sample at too a low frequency then spurious frequencies called aliases can be created in the reconstructed signal

Aliasing at the movies

Wheel turns not quite 1 circle per frame. Wheel seems to rotate slowly backwards

Wheels moving backwardsYou have probably seen this effect on TV or the cinema when a car moving forwards appears to have wheels that are rotating backwards

Software Demo Looking Less Often Activity 70S

Digitising a signal

The greater the number of bits the better the resolution

7=111

6=110

5=101

4=100

3=011

2=010

1=001

0=000

CD uses16-bitcoding

3-bit coding: an example

quantisationerror

sample

originalsignal

nearest digitalvalue chosen

001 100 101 110 111 110 100 011 100binary values

digital stream of bits

number of bits N

number of levels

2N

23=8 28=256 216=65536

3 8 16

8 256 65536

DigitisingSignals can be digitised by turning the sampled waveform into numbers.

•Sampling is done using an analogue to digital converter (ADC)•A Digital to analogue converter (DAC) can reverse the process•The diagram on the left shows that with 3 bits of information up to 8 levels can be stored (3 bits = 8 possible binary numbers)•Using more bits means more levels and a greater resolution

• A telephone uses 8 bits = 256 levels for each sample

• A high quality CD uses 16 bits = 65536 levels for each sample

Sampling and digitising 2

Chapter 3.1.2 – 3.1.3

Sending a fax

Time to send one page:

1 page = 2200 lines 1700 pixels per line = 3740000 pixels

digital line capacity = 64000 bits per second

01111000011110

A fax is a page of ink converted into black and white dots andsent as 1s and 0s

Convert page to black orwhite pixels. 200 pixels perinch. About 8 pixels per mm.

Convert pixels to stream ofbits, line by line.

time to send one page =

Run length compression:

Recode signal as runs of 1 or 0

11 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1111 11 1 0 0

2of 1s

13of 0s

8of 1s

2of 0s

Send these numbers instead.Typical compression 9 : 1

3740000 bits per page64000 bits per second

= 58 s or about 1 minute

Signal TransmissionA fax converts text and pictures into pixels one line at a time. This is slow and requires a lot of data to be transferred

•Slow information transfer rate

Sending an e-mail

An e-mail is a set of numbers coding for characters, and sentas 1s and 0s

Time to send one page:

1 page = 500 words = 3000 characters approx.

Thank you84 104 97 110 107 32 121 114 117

117 = 01110101

Computer and e-mailpackage encode letters asnumbers using ASCII code.

Code numbers stored asbinary digits. One byte (8bits) per character.

More coding:

E-mail also sends data which check and correct errors.

Messages are often divided into small packets, each sentby the best route available at the moment.

Packets have to be re-assembled into messages at thereceiving end.

= 3000 bytes= 24000 bits

digital line capacity = 64000 bits per second

Time to send one page = 24000 bits per page64000 bits per second

= 0.4 s approx.

D e a r s t u d e n t s ,

I h o p e t h a t y o u f i n d t h i s t e x t b o o ka s i n t e r e s t i n g t o r e a d a s w e h a v ef o u n d i l l u s t r a t i n g i t . A l o t o ft h o u g h t a n d d e d i c a t i o n h a s g o n ei n t o p r o d u c i n g t h i s , s o w e a l lh o p e a t I O P t h a t e a c h a n de v e r y o n e o f y o u p a s s y o u r A l e v e l s .G o o d l u c k t o y o u a l l .

T h a n k y o u

Signal TransmissionE-mail sends less information per page because it can encode letters as numbers instead of pixel by pixel.

•This means a faster information transmission time even if we use the same transmission rate (64000 bits per second) as the fax machine

SIGNALLING WITH EM WAVES

Chapter 3.2

Sending digital data 1

Channel Capacity needed

to send signal

Resolution (number of bits) of

each sample

Sampling rate (must be 2x highest

frequency in the signal spectrum)

Sending digital data 2•speech sampled at 8000 Hz•8 bits used per sample•64000 bits per second (64 kHz) need to be sent

Telephone

•sampled at 44.1kHz•16 bits used per sample•705600 bits per second to be sent (0.7 MHz)•2 Stereo channels doubles this to 1.4 MHz•This is in the medium wave radio band

CD Quality

LFlow frequency

navigation, radio beacons,long distance broadcasting

optical fibre, remote controls,bar codes, CD player

30 kHz

near infrared

MFmediumfrequency

HFhigh frequency

VHFvery highfrequency

UHFultra highfrequency

SHFsuper highfrequency

EHFextremelyhigh

far infrared

mid infrared

national broadcasting,aeronautical navigation

long distance broadcasting,amateur radio, maritime radio

radar, radio astronomy

FM radio, mobile radiocommunications

television, mobile telephonenetworks

satellite links, groundmicrowave links, radar

300 kHz

3 MHz

30 MHz

300 MHz

3 GHz

30 GHz

300 GHz

3 THz

30 THz

300 THz

10 km

1 km

100 m

10 m

1 m

100 mm

10 mm

1 mm

100 m

10 m

1 m

Communication wave bands

frequency wavelength

Waves all aroundLook at the size of TV aerials on the roofs of houses - they give you and idea of the wavelengths being received .

Usually the rods are half a wavelength long – a few cm

TV Ariel'sThe rods are a few cm long indicating that it is designed to receive waves with wavelengths of a few cm

PolarisationChapter 3.2.2 - 3.2.3

When the permitted direction of vibration or polarisation of the filter is parallelto the direction of the polarisation of the wave, it is transmitted by the filter.

When the permitted direction of vibration or polarisation of the filter is perpendicularto the direction of the polarisation of the wave, it is absorbed or reflected butnot transmitted.

PolarisationTV and Radio waves are polarised

To pick up a signal the receiving rods must be parallel to the electric field oscillations of the wave

Again looking at TV aerials will tell you the direction of polarisation

TV Ariel'sThe short Transverse rods indicate that this ariel is designed to receive waves that are horizontally polarised

Frequency SpectrumsChapter 3.2.3

Making MusicIf you are a Jazz Maverick and Electro-pop superstar its important that you know how to process sounds and music…

Oboe

Clarinet

Xylophone

Snare Drum

1000Hz Pure Tone

1000Hz and 3000hz combined

White Noise

Software Demo Cleaning up a sound Activity 210S

Multiplexing and Bandwidth

Chapter 3.2.4

8 bit sample 8 bit sample 8 bit sample 8 bit sample 8 bit sample 8 bit sample

Sending many telephone calls down the same pipe: time-division multiplexingOne callerSpeech sampled 8000 times per second: approximately at 100 s intervals

Many callersSlot 8-bit samples from other callers into the 100 s gap between samples from one caller

caller 1

caller 2

100 s

caller 1 caller 2 caller 3

other callers

100 s

Advantage of digital signalling: digits can easily be switched

100 s100 s 100 s 100 s

one sample

one sample

next sample

next sample

Microwave link sending digital pulses at 10 GHzTime to send 8-bit sample approximately 1 ns. Number of bits able to be sent in 100 s = 1 million

BandwidthBandwidth

The width of the frequency spectrum

of a signal

Telephone•3100 Hz (300 Hz to 3400Hz)

Music•20 to 40 kHz

The faster you need to transmit the

greater the bandwidth needed

Greater Bandwidth means the higher the

frequency band needed

Software Demo Bits per second and bandwidth Activity 260S

Bandwidth and sampling

Roughly speaking you need a bandwidth = to the maximum rate of transmission of bits

Maximum digital signalling rate in bits

per second = 2 x bandwidth needed B

Bandwidth B = 1/T where T is the time

one bit is “on”