The Digital DelugeLecture 2

Learning in RetirementDavid Coll

Professor EmeritusDepartment of Systems and Computer

Engineering

Winter 2009

• DigitalDigital means means discretediscrete (like whole numbers) (like whole numbers) and and AnalogAnalog means means continuouscontinuous (like physical (like physical properties such as temperature, volume, properties such as temperature, volume, etc.). etc.).

• The term The term analoganalog comes from early comes from early computers (circa WWII) used to solve computers (circa WWII) used to solve differential equations with continuous differential equations with continuous variablesvariables, ,

• as contrasted with as contrasted with discrete state machines discrete state machines (like an elevator controller) built from open-(like an elevator controller) built from open-or-closed switches or on-off digital circuitsor-closed switches or on-off digital circuits

Definitions (from whatis.com)

AnalogAnalog

• Using physical representationUsing physical representation

• Relating to a system, device that Relating to a system, device that represents data variation by a represents data variation by a measurable measurable physical quality physical quality such as temperature, such as temperature, volume, distance, weight, pressure …volume, distance, weight, pressure …

• Which is Which is continuouscontinuous in time or space and in time or space and valuevalue

Definitions

DigitalDigital

• Representing data as numbersRepresenting data as numbers– ProcessingProcessing– Operating on Operating on – StoringStoring– Transmitting Transmitting – Displaying Displaying

• Data in the form of numerical digits, as in a Data in the form of numerical digits, as in a digital computerdigital computer

• Representing a physical quantityRepresenting a physical quantity– such as sound, light, or electricitysuch as sound, light, or electricity

• by means of by means of samplessamples– taken at taken at discrete times discrete times (or (or placesplaces))– and given and given numerical valuesnumerical values

• usually in the binary systemusually in the binary system

– as in a digital audio recordingas in a digital audio recording– or in digital televisionor in digital television– or in digital photographyor in digital photography

In Communications

• AnalogAnalog is used to refer to systems with is used to refer to systems with signals that are signals that are continuouscontinuous in value and in value and timetime– such as AM and FM, where the electrical such as AM and FM, where the electrical

signals are representations of the signals are representations of the information signals.information signals.

Amplitude Modulation (AM)

)2cos()](1[)( tftmkAts cac

Phase or Frequency Modulation (FM)

))(2cos()(

))(2cos()(

0

dmktfAts

tmktfAtst

fcc

cc

In Communications

• DigitalDigital is used to refer to is used to refer to discrete-state, discrete-state, discrete-time discrete-time signals that can take on only signals that can take on only specific values at specific times;specific values at specific times;

• such as such as – sampled/quantized signals, sampled/quantized signals, – pulse modulated signals, pulse modulated signals,

• and to data communication signals in and to data communication signals in general.general.

Digital Modulation: Discrete in Time and Value

Parameters of Information Sources & Systems

• AnalogAnalog (continuous functions of time, (continuous functions of time, space, weight, …)space, weight, …)– voice, audio, image, video, temperature voice, audio, image, video, temperature

• Bandwidth – frequency (harmonics) rangeBandwidth – frequency (harmonics) range• Statistics – amplitude distribution, power, Statistics – amplitude distribution, power,

spectrum (frequency content, harmonics)spectrum (frequency content, harmonics)

• DigitalDigital (sets of numbers): (sets of numbers):– ASCII characters, computer words, …ASCII characters, computer words, …

• Bit Rate – bps, kbps, Mbps, Gbps, Tbps, Bit Rate – bps, kbps, Mbps, Gbps, Tbps, Ebps, … Ebps, …

How does Information Become “Digital”?How does Information Become “Digital”?

Digital Representation• Information that is naturally discrete, such Information that is naturally discrete, such

as state of a light switch (on-off), integers, as state of a light switch (on-off), integers, or text can be represented by binary or text can be represented by binary numbers in obvious ways.numbers in obvious ways.

• Text (as generated on a keyboard) is often Text (as generated on a keyboard) is often represented by 8-bit binary numbers.represented by 8-bit binary numbers.

• Speech may be represented by a pressure Speech may be represented by a pressure wave, which is continuous – in time and wave, which is continuous – in time and value – and has to be value – and has to be sampled and sampled and quantized to quantized to be represented digitally.be represented digitally.

Discrete Information

• Some information, such as numerals and Some information, such as numerals and characters is discrete and can be characters is discrete and can be represented “digitally” easilyrepresented “digitally” easily

• Take characters of the English Language Take characters of the English Language for examplefor example

• The American Standard Code for The American Standard Code for Information Interchange Information Interchange (ASCII)(ASCII) is the is the binary representation used in teletype binary representation used in teletype messaging and adopted as a universal messaging and adopted as a universal computer character representation. computer character representation.

“A” = 11000001

“a” = 11100001

10001101 = CR10001010 = LF

10000001 = SOH

10000010 = STX

10000100 = EOT

10000011 = ETX

“%” = 10100101

Formatting

Messaging

Serendipity• Early minicomputers such as Digital Early minicomputers such as Digital

Equipment Corporation (DEC) PDP Equipment Corporation (DEC) PDP machines used machines used teletypewritersteletypewriters as terminals as terminals

• They hadThey had– keyboards that generated ASCII code wordskeyboards that generated ASCII code words– printers that accepted ASCIII code words printers that accepted ASCIII code words

and and – punched paper tape I/O that could be used to punched paper tape I/O that could be used to

save and replay messages.save and replay messages.

• The ASCII code set includingThe ASCII code set including– text formattingtext formatting

• CR and LFCR and LF– and message formattingand message formatting

• SOH, STX ETX, EOTSOH, STX ETX, EOT

• Became the way computer communications Became the way computer communications over leased and dial-up telephone lines over leased and dial-up telephone lines startedstarted

• Except for a bunch of computer geeks who Except for a bunch of computer geeks who used Sun Microsystems workstations which used Sun Microsystems workstations which had a different communications scheme had a different communications scheme built-in.built-in.

Common Sense Digitization of Analog Information

• All continuous signals can be represented All continuous signals can be represented by a collection of numbers to any degree of by a collection of numbers to any degree of accuracy by accuracy by – sampling often enough sampling often enough and and – using enough quantization levels*using enough quantization levels* to represent to represent

the signal value at the sampling instants.the signal value at the sampling instants.

– ** determined by the number of digits in the determined by the number of digits in the representationrepresentation

Analog-to-Digital Conversion

• Two stage processTwo stage process• SampleSample

– Sampling TheoremSampling Theorem– Nyquist RateNyquist Rate

• QuantizeQuantize– Precision, SNR (% average Precision, SNR (% average errorerror))

– Note: a digital representation of an analog Note: a digital representation of an analog value always has errorvalue always has error

The Sampling Theorem

• Shannon’s Sampling Theorem states that Shannon’s Sampling Theorem states that – any bandlimited signal may be represented by any bandlimited signal may be represented by

samples taken at a rate of twice its highest samples taken at a rate of twice its highest frequencyfrequency*, and *, and

– may be may be reconstructed reconstructed without errorwithout error if the if the appropriate interpolation functions are used**.appropriate interpolation functions are used**.

* Twice the highest frequency is called the * Twice the highest frequency is called the Nyquist RateNyquist Rate..

** Physically unrealizable sinx/x or (sinc) functions.** Physically unrealizable sinx/x or (sinc) functions.

Nerd AlertNerd Alert

Impulse Sampling

Reconstruction

Summary

• All signals can be represented by a All signals can be represented by a collection of numbers to any degree of collection of numbers to any degree of accuracy by sampling often enough and accuracy by sampling often enough and using enough quantization levels to using enough quantization levels to represent the signal value at the sampling represent the signal value at the sampling instant.instant.

Summary (for irrepressible nerds only)

• Shannon’s Sampling Theorem Shannon’s Sampling Theorem states that states that any strictly bandlimited function may be any strictly bandlimited function may be presented by sampling at a rate that is at presented by sampling at a rate that is at least twice as fast as the highest frequency least twice as fast as the highest frequency in the signal, and that it may be recovered in the signal, and that it may be recovered without distortion without distortion by passing the (impulse) by passing the (impulse) samples through an ideal low-pass filter samples through an ideal low-pass filter with a bandwidth equal to that of the signal.with a bandwidth equal to that of the signal.

Quantization

• For processing, storage or communication, samples with infinite precision must be quantized

• Such that a range, or interval, of values is represented by a single, finite precision, number

• For example, by a finite binary number.

Quantization

7

-3

12

7

5 5

-3-2

-4-3

-2

7 7

32

6

7

43

11

time

Reconstitution

time

-2

-3

-4

Quantum Boundary

Quantum Boundary

Reconstruction ValueActual Value

ERROR-3

7

-3

12

7

5 5

-3-2

-4-3

-2

7 7

32

6

7

43

11

Quantization Error (for nerds and audiophiles)

• The quantization error depends on the number of distinct quantization intervals used.

• If N binary digits are used, the number of distinct intervals is 2N.

• The signal-to-quantization-error ratio is about (6N + 1.8) dB.

Binary Representation

• Once information is discretized, or sampled, a number can be assigned to represent the value of each sample.

• The number can be expressed as a binary number, e.g., 2009 is

1024 + 512 + 256 + 128 +64 + 32 + 8 + 4 + 1

1x 210 + 1x 29 + 1x 28 + 1x 27 + 1x 26 +1x 25 +1x 23 + 1x 22 + 1x 20

11111101101

SummarySummary

The basis of the Digital Deluge is The basis of the Digital Deluge is the universal adoption of a the universal adoption of a technology that can create, process, technology that can create, process, and communicate information that is and communicate information that is represented in digital form.represented in digital form.

• So much for Digital RepresentationSo much for Digital Representation• Now, let’s look at Digital Information Now, let’s look at Digital Information

TechnologiesTechnologies• But, firstBut, first

• Let us pause for a short break ….Let us pause for a short break ….

Let us look at the Digital Technologies

• CommunicationsCommunications• ComputingComputing

Digital Communications• We have We have

– Sources of InformationSources of Information• That create informationThat create information

– Destinations for InformationDestinations for Information• That use informationThat use information

• and we haveand we have– Communications NetworksCommunications Networks

• That provide connectivity between themThat provide connectivity between them

• We also have TerminalsWe also have Terminals– That interface (connect) the Sources and That interface (connect) the Sources and

Destinations to the Networks.Destinations to the Networks.

A Taxonomy of Telecommunications

• SourcesSources• ChannelsChannels• DestinationsDestinations

ChannelsChannelsSourceSource

DestDest

DestDest

Term

Term

Term

Term

Term

Term

What are “Digital” Communications?

• Modern Telecommunication Systems are designed to accept and deliver information made up of sequences of binary signals.

• These systems and the connections through them are enabled and controlled by computers.

What is Special About NOW?Why the Deluge NOW?

• Realization of the Telecomm Dream

– Unified Communications• ubiquitous high speed, multimedia, reliable,

standardized networks– The All-IP Multimedia Network – The Internet and the WWW

– Ubiquitous Broadband Access• Wired (FTTP)• Wireless(Cellular/WLAN)

More on Communications

• We will discuss communications later when We will discuss communications later when we look at delivering digital information.we look at delivering digital information.

Computers: Universal Digital Processing Machines

• Computers are universal digital machines Computers are universal digital machines that can that can – accept information in digital form accept information in digital form – store it store it – process it in many waysprocess it in many ways– output it to various devicesoutput it to various devices– display it display it – communicate it communicate it

• All under control of a set of pre-determined All under control of a set of pre-determined steps called a program.steps called a program.

The Evolution of the Computer

• Intelligent Information Agents– Communications, Processing, Control– Programmable – Powerful Hardware: speed, memory– Handheld/Mobile– Robotic

• autonomous tasks• in touch with local environment

Terminals and Switches

– Terminal EquipmentTerminal Equipment• the sources and destinations of information, the sources and destinations of information,

are digital machines, i.e., computers, in the are digital machines, i.e., computers, in the broadest sense.broadest sense.

– Network Switches are also computers.Network Switches are also computers.

• Software Development– Highly evolutionary – Use of complex components– Standardization

Intelligent Agent: Telematics

Com

munications

Processor

A &

D I/O