Day 3

Fundamentals of Data and Signals

What is Data• Data is any type of information:

– For Example:• A word document• A web page• An image• A conversation

– We are surrounded by data.

Digital Data• Digital data - discrete.

– At each moment in time the data must be at one of many discrete points.

– It CANNOT be in between.– E.g

• Lights are either on or off.• Traffic signals can only be Red, Yellow or

Green. The traffic light has no way of showing you how close it is to turning red from yellow. It doesn’t show different shades of orange in between.

• Digital clock

Analog Data• Analog data - Continuous

– Found in the real world. • Voices, songs, pictures taken on a film camera…

– Analog data is by its very nature continuous. At each moment in time the data can be at an infinite number of different points between a min and max value.

– E.g.• A jar of peanut butter has an analog amount of

peanut butter in it. You can always remove some amount, and replace ½ of it. Only our instruments limit our ability to measure the amount of peanut butter in the jar. For example there may be 10.2842042804280284008293320302844324732 ounces

• Analog clock – sometimes.

Data vs. Signals• Data is the information we want to

send• A signal can be used to send data.

– Lets imagine we all have frequency generators handy

– How could we use that to send the following data:• Yes/No• The numbers between 0 and 9 (key lock)• The alphabet• A photograph• A piece of music?

Representing data in a signal• A signal has 3 attributes

• Amplitude– How tall the graph gets

• Frequency– How long it takes the graph to make 1

complete cycle.– How many times it makes a complete cycle

in a given period of time

• Phase– A wave form is typically continuous. A

phase change means the wave jumps forward or back in time and thus makes an abrupt shift.

• We can use all 3 attributes to “Encode” data.

Amplitude (Measured in Db)10 Rustle of leaves

20 Whisper

30 Quiet Conversation

50 Typical Outside Conversation

70 City Street

90 Underground train passing

120 Jet aircraft taking off – Pain threshold

Loss and gain in dB• When we transmit a signal it fades the

further it goes.– Human voice can only be heard up to a

certain distance. If it needs to be heard further, you must use more amplitude.

• A gain is called amplification• A loss is called attenuation• A 3dB loss means a signal has lost ½ its

power.– E.g A 100W signal has 3dB of attenuation

during transmission, 50W will reach the other side.

• Likewise a 3dB gain means it doubles its power.

• Decibels are a logarithmic scale.

Musical Instruments FrequencyPiano 27.5 – 4,186 Hz

Cello 65.41 – 987.77 Hz

Flute 261 – 3,349 Hz

Guitar 82.41 – 880 Hz

Bass Singer 87.3 – 349 Hz

Baritone Singer 98 – 392 Hz

Tenor Singer 130 – 494 Hz

Soprano Singer 246 – 1175 Hz

Telephone• Human Range 20Hz – 14,000Hz• Most voice conversations happen

between 300Hz and 3400Hz.– The telephone uses these exact

numbers to filter frequencies. Hence if you hit a high note on a piano and have your friend try to hear it on the other end, they will hear nothing.

Ranges• The spectrum of a signal is the

range of frequencies it goes through from min-max.

• The bandwidth of a signal is the difference between the lowest and highest frequencies– Effective bandwidth is how much of

that you can use

Analog Signals• An analog signal is a continuous

signal. – One example of an analog signal is

when you encode music/voice into electricity (microphone/stereo).

– The electricity varies exactly with the frequency of the voice.

• An analog signal encoding analog data is the only way to truly capture the data without loss.

Digital Signals• At each time slice must be in

discrete places. – CDs/DVDs are examples of a digital

signal recorded onto the CD

Analog data on digital signal and vice versa• You can record any of the

following:– Analog Data

• Analog Signal• Digital Signal

– Digital Data• Analog Signal• Digital Signal

– We have many examples of each in everyday life

Examples • Analog Data stored in an analog

signal– Television, Radio

• Analog Data stored in a digital signal– CD, DVD

• Digital Data stored in an analog signal– Modem

• Digital Data stored in a digital signal– LANs

Encoding the alphabet• We earlier asked how can you send

letters of the alphabet via frequency.• Now, how would you do it if you only

had a “on” or “off” light switch.– Clearly there are more than 2 letters in the

alphabet, so you’ll have to use a sequence of “on” and “offs” to send the data.• Let’s assume the duration the light is on

doesn’t matter for each on or off.

• Turns out you’ll need 7 “on’s” and “off’s” to capture each of the 26 letters + 26 upper case, plus basic things like spaces, commas, periods.– Each “on” or “off” is called a BIT.

Ascii• Encode letters into 1’s and 0’s

– Each letter takes 7 bits to encode.– Typically an 8th bit is included for

error checking• Or can be used for “extended ascii set”

– Ascii Chart• http://www.lookuptables.com/

• For example A is decimal 65 which translates into binary as 1000001

Unicode• Ascii works great as long as you

speak English, but if you need different character sets, you’ll need extended ascii or Unicode

• Unicode uses 16 bits to represent different values

• Charts:– http://www.unicode.org/charts/

Spread Spectrum Technology• Your cordless phone at home uses

this.• Lets imagine that we both have a

code book– 12, 19, 42, 72, 11, 2, 8, 99, 1, 34, 71, 23

• We agree that we’ll start at the second number (19) and we use that number of Khz to transmit on for 2 seconds. Then we’ll jump to the next Khz.

• Makes it very difficult for anyone to listen to your conversation and make any sense out of it.