Analogue and Digital Signals

SL – Option C.1

Signals

• When talking about electronics we will talk about ‘signals’– This is simply the transfer of information from

one place to another– An electrical signal is when information is sent

by a changing electric field

Analogue Signals

Analogue Use

• Sound transmission is an example of an analogue signal– When you speak into a microphone the

change in pressure causes the inside of the microphone to vibrate and change the potential difference

– This signal can be fed through an amplifier which will increase the strength of the signal reproducing the signal but louder

Analogue Storage• Vinyl Records

– A record is made of plastic that has a thin groove cut into it by a needle that moves at the same frequency as the sound it is recording

– Playback involves a needle connected to a circuit that follows the grooves

Analogue Storage

• Audio Tape– A tape also uses an analogue signal to store

data. Instead of varying grooves however, the tape, which is made out of magnetic material, has varying magnetic fields.

– To record, the tape is run through an electromagnet which varies the field at the same rate as the sound signal

Digital Signals

• A digital signal does not vary over time but rather changes from one discrete value to another.– In a circuit with a switch and a light bulb, the

bulb is on when the switch is closed and off when the switch is open

Digital Signals

Binary Number Systems

• “There are 10 kinds of people in the world, those who understand binary and those who don’t”

• Digital Signals are encoded/stored using the binary number system– This is a system of 1’s and 0’s– Our normal numbering system uses a

base-10 system while the binary system uses a base-2 system

Binary Number System

Base 10 3 2 1 0

1000 100 10 1

Base 2 3 2 1 0

8 4 2 1

Decimal Binary

1 00000001

2 00000010

3 00000011

4 00000100

5 00000101

Binary Number System

• In the binary number system, each 1 or 0 is called a bit– There are 8 bits in a byte

• An 8 bit system has 8 places 00000000• A 128-bit encryption has 128 places• With the 8-bit system all western characters can be

coded• Each symbol (letter, number, etc.) takes up 1 byte

of memory

Bit rate

• Bit rate can be found one of two ways-– Bit rate = 1/t (where t is the number of

seconds in each bit)– Bit rate = f x n (where f is the frequency and

n is the number of bits per sample)

LSB and MSB

• Least significant bit – bit that is farthest to the right– Determines whether the number will be even or

odd.

– Changes with any small number change

• Most significant bit – bits farthest to the left– Don’t change unless there is a large number

change

– Often 000

• 0000101 LSB is 1 and MSB is 0

Converting to Binary

• Long division method…

• 156

• 53

• 1652

Converting from Binary

• Addition method…

• 10011011

• 11101010

• 00001111

Analogue to Digital Conversion

• Analogue signals can be converted to digital by breaking the analogue signal into discrete values (quantized)– The more values that are

used, the more accurate the digital signal will be, but more storage space will be required

Analogue to Digital Conversion

• The quantized values can then be converted into binary– If the quantized values range from -6V to +6V

this can be represented most easily by the numbers 0 – 12

– A 4-bit system can be used to represent these numbers (0000 – 1100)

– As long as the bit rate is known, the signal can then be converted back.

Sampling Rate

• The sampling rate is how often the quantized value is measured and recorded– The higher the sampling rate, the more

accurate the digital conversion will be– Nyquist theory states that to record a certain

frequency the sample rate needs to be at least 2x the frequency

• This is so at least 1 peak value and 1 trough value can be recorded

Sample Rate

• Here there are 22 samples taken for every cycle. What if there were only 2? 4? Etc.?

This is an analog audio signal at 500Hz. -Convert this to a digial signal with a sample rate of 357Hz

Then convert it back to a analog signal

This is an analog audio signal at 500Hz. -Convert this to a digial signal with a sample rate of 1kHz

Then convert it back to a analog signal

Time Diversion multiplexing

• There is dead time between each signal sent, so using this method other signals can be sent so the “dead time” isn’t wasted.

Advantages of digital communication

• Digital signals can be regenerated perfectly (no noise)

• Digital circuits are relatively inexpensive• Error correcting codes can be applied to the signal

to eliminate errors• Signals can be encrypted• Signals can be stored and processed by

computers• Digital signals can be stored on CD’s and DVD’s• Digital signals can be compressed

End

Storage on a CD

• Basic structure of a CD

– Information is stored on the CD as a series of bumps and flats pressed into the aluminum

Storage on a CD

• The data is ‘read’ by a laser that shines along the tracks– The light reflected off of the flat sections will

be read as a ‘1’, – If the pit/bump is just the right depth the light

reflected off will destructively interfere with itself and the lack of light will be read as a ‘0’

Storage on a CD

• Destructive Interference Review:

– The reflected wave must be a ½ λ (π) out of phase

Storage on a CD

• How deep do the pits need to be?– If light with a wavelength of 780nm is used to

read a CD, what is the minimum depth the pits need to be?

• The light that hits the pit travels 2d farther than the light reflected from the flat portions.

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Reading a CD

• So ‘0’s are actually read every time depth changes – Both the start of a pit and the end

CD vs. DVD

• CDs can hold about 650MB of info while DVDs can hold about 4.7 GB– DVDs use light with a wavelength of about

640 nm which means that smaller (thinner) pits can be read

– This is because of the resolution of the light, shorter wavelengths can be resolved (separated) more clearly

Analogue vs. Digital Storage

• Benefits of Digital– Quality and Corruption

• Digital data is far less likely to be corrupted– On a tape the magnetic fields can fade, on an LP the tracks will

wear

– Even if a CD wears, the distinction between a 1 and a 0 is still apparent

– Accurate Reproducibility• Data can be stored and retrieved with much more accuracy

in digital form

– Greater Portability and Capacity– Easier to Manipulate

Analogue vs. Digital Storage

• Benefits of Analogue Storage– With analogue there is the potential for infinite

signal variation• Digital is constrained by the number of bits

– Processing and retrieving equipment is simpler (not necessarily easier to use)

Implications of digital data storage

• What possible negative could all this cool technology have?