1. Topic 14.1: Analogue and digital signals
Digital technology
Topic 14.1: Analogue and digital signals

2. Digital technology 14.1 Analogue and digital signals
14.2 Data capture; digital imaging using charge-coupled devices (CCDs)

3. Compact Disks
CDs were first introduced in the early 1980s, their single purpose in life was to hold music in a digital format.
To understand how a CD works, you need to first understand how digital recording and playback works and the difference between analog and digital technologies

4. What are analogue signals?
Analogue is a transmission standard that uses electrical impulses to emulate the audio waveform of sound.
When you use a phone, the variations in your voice are transformed by a microphone into similar variations in an electrical voltage and carried down the line to the exchange.

5. Electrical signal of a conversation

6. At the other end
The electrical signal is then turned into sound by a speaker and you can hear the voice
The electrical signal is not perfect and there will be ‘noise’, often heard as a hiss

7. Problems The electrical copy is not perfect
The electrical wires have resistance and so the voltage will decrease
This limits how far the signal can be sent as the signal will be too low compared to the noise

8. Analogue signal with medium signal to noise ratio

9. A solution?
It is difficult to distinguish between the analogue signal and the noise
A solution is to turn the conversation into a digital signal.
This is an analogue to digital conversion

10. What are digital signals?
Digital - A method of storing, processing and transmitting information through the use of distinct electronic or optical pulses that represent the binary digits 0 and 1.

11. Signal Consisting of 1 Hz, 5 Hz and 10Hz
Sampled at 2 Hz
1 Sec

12. Signal Consisting of 1 Hz, 5 Hz and 10Hz
Sampled at 5 Hz
1 Sec
Here we seem to obtain a good sin wave at a frequency which was not present in the original signal. This is called ‘Aliasing’.

13. Signal Consisting of 1 Hz, 5 Hz and 10Hz
Sampled at 10 Hz
1 Sec

14. Signal Consisting of 1 Hz, 5 Hz and 10Hz
Sampled at 20 Hz
1 Sec

15. Signal Consisting of 1 Hz, 5 Hz and 10Hz
Sampled at 40 Hz
1 Sec

16. Conclusion
Complex signals are made up of many sine waves of different Frequencies and Amplitudes.
If we wish to sample these signals in such a way as to be able to reconstitute the original signal, the sampling rate must be at least twice the maximum frequency present.
A sampling rate of twice the maximum frequency present is called the ‘Nyquist Rate’ (Each sampled signal has its own Nyquist Rate)
For satisfactory sampling:
If the sampling rate is too slow, ‘Aliasing’ can occur.

17. Sampling Accuracy or ‘Quantisation’
More Easily explained by looking at a small section of signal

18. If the signal is to be transmitted digitally, the height of each sample must be represented by an exact number of binary digits (bits).
We must therefore have a scale on which we measure the height, and the height of each sample must be rounded up or down to fit an exact value on this scale.

19. Accurate Sampling

20. Medium Sampling

21. Poor Sampling

22. Very Poor Sampling

23. Conclusion
1. Clearly higher sampling accuracy gives a more faithful reconstituted signal.
2. But sampling more accurately means it takes more binary digits to store or transmit each sample.
3. So there is a compromise to be reached between accuracy of sampling and number of bits needed.
4. But if the ‘faithfulness’ or ‘fidelity’ is such that the human ear can’t tell the difference there is no point in improving it further

24. Noise and signal recovery
Why do we go to the trouble of digitising signals when it automatically involves a compromise….
Between fidelity and quantity of binary digits which must be stored/transmitted

25. A Noise Signal

26. Analog Signal with Noise (Large Signal to Noise Ratio)

27. Analog Signal with medium Signal to Noise Ratio
The signal can be recovered reasonably well by smoothing
(but each time we do this the corruption is increased.)

28. Analog Signal with small signal to noise Ratio
Even if we try to recover the signal by smoothing it is corrupted.

29. Digital Signal

30. Digital Signal with large signal to noise ratio
The signal only consists of ‘1’s and ‘0’s so it can be recovered exactly.
This can be done as many times as necessary.

31. Summary
1. All signals which are transmitted or processed in any way (e.g. amplified) are subject to corruption by noise.
2. Once an analogue signal has been corrupted by noise it is impossible to recover it exactly.
(The greater the signal to noise ratio the less accurately the signal can be recovered.)
3. Quite badly corrupted digital signals can be recovered exactly because they only consist of ‘1’s and ‘0’s and these can be reconstructed easily.
4. Digital signals only become impossible to recover when the signal to noise ratio (S/N) is such that a ‘1’ could be mistaken for a ‘0’. That is, when S/N  1.
5. Noise is a random quantity, so large spikes appear very occasionally which could corrupt a single bit. This problem is overcome by adding extra information to the digital signal which allows ‘error checking’

32. Decimal numbers
The decimal number system (base 10) is the most widely used number system.
It uses ten different digits:
0,1,2,3,4,5,6,7,8 and 9

33. Binary numbers
The binary number system (base 2) is the most widely used number system in computers
It uses two different digits:
0 and 1
Each binary digit is called a ‘bit’.
For example, the number is 8 bits long.

34. Least-significant bit (LSB)
In computing, the LSB is the bit position in binary number giving the units value.
In this 8 bit binary number the highlighted number is the LSB:
The LSB is sometimes called the right-most bit.

35. Most-significant bit (MSB)
In computing the MSB is the bit position in binary number having the greatest value.
In this 8 bit binary number the highlighted number is the LSB:
The MSB is sometimes called the left-most bit.

36. Converting decimal numbers into binary numbers
To convert a decimal number into its binary number the number is divided by 2.
The remainder is the LSB.
The integer result is divided by 2 again.
The new remainder is the next MSB.
This repeated until the result of further division becomes zero.

37. Example Converting 25 to binary: =11001 Operation Remainder 25/2=12 1
12/2=6
6/2=3
3/2=1
1/2=0

38. Converting binary numbers into decimal numbers
To convert a binary number into its decimal number the you start from the left number, double the number and add the next number.
The answer is doubled and the next number is added.
This is repeated until no more numbers remain.

39. Converting binary numbers into decimal numbers
What is in decimal form? =
= 23
Binary number 1
Place 4 3 2

40. Example Operation Remaining digits 11001 (0x2)+1=1 1001 (1x2)+1=3 001
11001
(0x2)+1=1
1001
(1x2)+1=3
001
(3x2)+0=6 01
(6x2)+0=12 1
(12x2)+1=25
Converting to decimal: 25

41. Analogue
Digital
LPs, cassette tapes
CDs, DVDs,
hard discs
information is stored in continuous, variable form
information is stored in discrete form
LP: minutes per side; 2 sides
CD: approx 80mins
needle travels fastest on the outside edge
change their speed of rotation to provide constant linear velocity
Play from the outer radius inwards
Play from the inner radius outwards

42. Storing Analog signals
There are two main ways of storing analogue signals,
either as variations in the surface of a plastic (vinyl) disc - a record, or
variations in the arrangement of magnetic particles attached to a plastic tape - reel to reel tape or cassette tape.

43. For a record, a spiral groove is pressed into the surface of the vinyl disk.
The depth of the groove varies with the value of the analogue signal being stored.
To recover the analogue information from the disc, the disc is rotated at a constant angular speed and a stylus is placed into the groove.
As the disc rotates, the stylus moves along the groove picking up the variation in depth.
A magnet attached to the stylus moves in and out of a coil of wire with the depth variations, so turning this into an analogue electrical signal.

44. For a tape recorder, the analogue signal is stored on a very thin piece of plastic (mylar) coated in very fine particles of
magnetic iron or chromium oxide.
The tape passes at a constant speed in front of a tape head.
The analogue signal is applied to the coil in the tape head.
This causes a strong magnetic field to develop in the gap at
the front of the tape head, which is in contact with the tape.
The magnetic particles on the tape align with the magnetic
field in the gap, and maintain this alignment after the tape has
moved past the head.

45. On playback, the tape again passes in front of the tape head, but this time the magnetic oxide on the tape causes a small voltage to be generated in the coil of the tape head. This small voltage is then amplified by an amplifying system.
The most popular form of analogue tape recording was the Compact Cassette system in which the tape was 3.81mm wide and moved at a speed of 4.76cm/s across the tape head. A typical C90 cassette, which held 45 minutes of information on each side, contained approximately 129m of tape.

46. Storing digital information
The most popular methods of storing digital information include Compact Disks (CDs and DVDs), Hard disks (as in Computer systems) and solid state flash memory (Memory sticks and cards).
At the time of writing the first 1TB (Terabyte; 1 byte = 8 bits) hard disks are becoming available (capable of storing around 300 full length feature films) while memory cards and sticks are now available with a capacity of 16GB.

47. By comparison, a CD will hold 700MB of information and a DVD up to 9GB of information.
All digital storage media read and write data one bit at a time. An interesting development in the storage of digital information is the holographic disk, which instead of reading and writing one bit at a time, handles 216 bits of data each time the read/write laser flashes.

48. A hard disk consists of several very flat disks coated with ultra fine coating of magnetic oxides. These disks rotate very fast, some as fast as 15000rpm.
The recording and replay system is similar to that of the magnetic tape, except that, because the disks are rotating so quickly, the read/write heads just skim the surface without touching the disk.
A major advantage of magnetic disk systems over magnetic tape is that the data can be accessed randomly, since the head can quickly move to any part of the rotating disk.

49. Solid state flash memory cards are essentially very complex integrated circuits containing billions of NAND (or NOR) gates arranged as bistable latches with each latch storing 1 bit of information.
As the manufacturing techniques of integrated circuits continues to develop, it is quite likely that these will eventually replace hard disk systems.

50. A CD consists of polycarbonate plastic impressed with a single spiral track of data, 0.5 microns wide with 1.6 microns separating one data track from the next, circling from the inside of the disc to the outside. Once the plastic has formed it's coated with reflective aluminum and a clear acrylic layer to protect the aluminum.

51. The laser beam scans the spiral from the centre of the disk and is reflected from the tracks, either weakly due to scatter (logic 1) or strongly due to simple reflection (logic 0), and is detected by a photo-transistor.

52. The CD data is arranged in spiral tracks some 1.6m apart.
The pits are a minimum of 0.83µm long, 1.6µm apart and 125nm deep.
DVD pits are 0.4microns, 0.74 microns apart and 120nm deep.
The space between two holes is called an island.
A CD will hold around 700MB of data while a single sided standard DVD will hold around 4.7GB of information.

54. Light that strikes the areas of the CD without pits is reflected normally.
Light that strikes a pit undergoes destructive interference with the light reflected from the area surrounding the pit.
This occurs because the depth of each pit is one quarter of the wavelength of the laser light.
Do you know why ¼ of wavelength?

55. The height of the pit is 1/4 of the wavelength of the laser light when travelling in polycarbonate, so that light reflected from the pit has a phase difference of one-half wavelength.
The light reflected from the bump and from the surrounding land cancel each other out.

56. The wavelength of the laser radiation
for a CD is 780nm,
for a DVD it is 650nm and
for the new high density DVDs it is 405nm.

57. Pit depth of a CD
The laser used to read a CD emits radiation with a wavelength of 780nm in air. However, the polycarbonate layer on the bottom of the CD has a refractive index of approximately 1.56, and so when the laser light passes into the polycarbonate layer its wavelength is reduced to .

58. Initially CDs were designed to operate by interference of the light.
The light reflected from a island had a path difference of /2 compared to light reflected from the surrounding area, resulting in destructive interference and so a reduction on the light intensity at the detection system.
This means that the height of each bump must be /4 of the wavelength of the light in the polycarbonate layer, i.e. 125nm.

59. Such systems worked well for CDs which were "pressed" from a master.
However, with the development of Writeable CDs (CD-Rs), it was not possible to produce bumps with such accuracy and so the detection system on CD readers developed to respond to changes in intensity, with a logic 0 corresponding to a reflection of greater than 70% and a logic 1 corresponding to a reflection of less than 25%, rather than complete cancellation of the reflected light.
It is for this reason that old CD players will not reliably read CD-Rs.

60. Information storage
Advantages of storing information in a digital form are:
Quality
Digital data has the major advantage that the quality does not deteriorate no matter how many times it is copied.
With analogue data, noise is added to the information each time it is copied, resulting in a degradation of the quality of the information.

61. Reproducibility Retrieval speed
Digital data can be copied quickly and readily. Error checking and correction ensure it does not become corrupt. It is not possible to apply error checking and correction techniques to analogue data.
Retrieval speed
Digital data can be retrieved at high speed especially from Random Access Memory devices, e.g. hard disk drives, CDs, DVDs, NAND gate memories, etc. Retrieval of data from tape systems is much slower and is comparable to the speed of access with analogue systems.

62. Portability Manipulation of data
A further major advantage of Digital data is that it can be encrypted, i.e. put into a form so that a special decoding 'key' is needed to be able to access the information. This prevents unauthorised reading of the information by anyone other than those with the encryption key. It is not possible to encrypt analogue data without seriously degrading the quality of the information.

63. Advantages and disadvantages
Advantages of Digital:
Less expensive
More reliable
Easy to manipulate
Flexible
Compatibility with other digital systems
Only digitised information can be transported through a noisy channel without degradation
Integrated networks
Disadvantages of Digital:
Sampling Error
Digital communications require greater bandwidth than analogue to transmit the same information.
The detection of digital signals requires the communications system to be synchronised, whereas generally speaking this is not the case with analogue systems.

64. Advantages and disadvantages
Advantages of Analogue -
Uses less bandwidth
More accurate
Disadvantages of Analogue -
The effects of random noise can make signal loss and distortion impossible to recover

65. Issues for society of ever-increasing data storage
As it becomes possible to store more and more data there are implications for society:
Storage:- It is estimated that the world generated 161 billion gigabytes (161 exaBytes) of digital information in This will only increase year on year.

66. Cataloging all of the digital information available is a major problem
Cataloging all of the digital information available is a major problem. It is likely that there are many identical copies of the same information held on separate systems. Accessing the right information is a major issue and the scale of the problem again increases year on year.
Moral:- personal data stored and available very quickly e.g. police records, credit ratings, mobile phone records, internet records.

67. Ethical:- data bases 'talk' to each other - data can be matched so that a complete set of personal data can be easily obtained. The recent growth in closed circuit television cameras (CCTV) means that where ever you go in a large city you are likely to be captured on camera. These images are stored digitally and so can be used to monitor where you go.

68. Piracy:- Video and audio data can be copied flawlessly leading to a large market of illegal music and film discs. This deprives the copyright holders of the materials of important revenue which they are then not able to use to produce more music/films.

69. Data centres:- To store all of the online digital information requires large 'Data Centres' which are packed with racks of high performance computers (servers). These consume a significant amount of power both to operate and to keep cool. It is estimated that 2.5% of the green house gases produced by the UK is as a result of the operation of data centres.

70. Waste:- The life cycle of a computer is approximately four years
Waste:- The life cycle of a computer is approximately four years. Even though the computer may still be working, advances in software and storage capacity result in it being necessary to upgrade to a new machine. The disposal of this redundant equipment poses a serious problem. As well as the disposal of the hardware there is also a major disposal problem associated with the general waste of resources, e.g. the polycarbonate thrown away in CDs each year.

71. Back up of data:- With such huge quantities of data produced each year, a major problem is the backing up of this data to ensure it is not lost by hardware failure, software or operator errors.
One click of a mouse button could completely destroy years of data!