1. Chapter 5 Analogue to Digital
Riaz Esmailzadeh

2. Signal Sampling Miner’s patent on sampling commutator
Luke’s narrative of theoretical development
Rule of thumb development and acceptance
Theoretical formulation
Mathematical discovery
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3. Analog Signals Natural phenomena are continuous waveforms Seismometer
Temperature
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4. Discrete Representation
Temperature can also be represented as a series of discrete numbers
Which of these two (three) representations is most accurate?
What should be the frequency of discrete representation?
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5. Example What is the frequency of this signal
Which of the discrete representation is more accurate?
Amplitude
Time
(B)
(A)
(C)
(D)
1 s 1 -1
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6. Nyquist Theorem
The necessary sampling rate is given by Nyquist Theorem, named after Harry Nyquist a scientist from the Bell Labs
Sampling rate must be more than twice the largest frequency component of the analogue signal
This is known as Nyquist rate
Assuming the largest frequency of the previous signal is 5 Hz, sampling rate should be 10 Hz. 1 1
Amplitude
Amplitude
1 s
Time
1 s
Time -1
(A) -1
(B)
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7. Quantization Levels
Each sample needs to be represented by its amplitude
The sample size must be closely represented by a number – this is known as quantization
We may represent the samples by { , , , , , , , , , }
Or by: {0.913, 0.663, 0.137, , , , 0.824, 0.287, , 0.995}
Which of these two representations is more efficient? 1
Amplitude
1 s
Time -1
(B)
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8. Binary Representation
In practice, digital transmission is carried out using binary numbers (that is using only ‘0’s and ‘1’s) rather than decimal
The signal levels are converted to binary numbers using a set number of quantisation levels
4 bits are used for each quantization level to represent the signal: {1111, 1101, 1001, 0011, 0000, 0100, 1110, 1010, 0000, 1111}
The receiver can reproduce the analog signal with the knowledge of sampling rate, quantisation levels and minimum-maximum range 1 1
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
Amplitude
Amplitude
Time
Time
1 s -1
(A) -1
(B)
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9. Quantization Error and Number of Bits
If the number of quantization levels is not large enough, then there will be quantization errors
Here the first and the last samples are both represented by 1111, whereas their amplitude is clearly different.
More accuracy can be obtained if more quantization levels are used
At cost of more bits
Two factors determine the number of bits
Required accuracy
Device structure and telecommunications protocol.
Usually as a multiple of 8 bits or 1 byte 1
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
Amplitude
Time -1
(B)
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10. Why Digital?
Analogue transmission of signals is degraded by the presence of noise in the network
Electronics
Exchange
Noise S
Noise is a physical process and although efforts may be made to make it small, it can never be removed
Noise accumulates at each electronic stage of transmission
For example: long distance calls usually had a worse quality compared with local call
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11. Noise Accumulation An example of noise accumulation is shown here.
Digital communications provides a way to reproduce signals at each exchange and therefore stop accumulation of noise
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12. Digital Signals and Noise
Consider the following digitals signals and the effect of noise on it 1 -1
Digital Stream
Noise Signal
Combined Signal
Time
Amplitude
This digital signal may be detected without error at a receiver and perfectly reproduced. Here SNR ≈ 10.
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13. Errors (SNR = 0.5)
Consider the following signal when noise is relatively increased 1 -1
Digital Stream
Noise Signal
Combined Signal
Time
Amplitude
When noise level is high, then some bits may be received in error.
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14. Larger Noise and more Errors (SNR = 0.1)
Consider the following digitals signals and the effect of noise on it 1 -1
Digital Stream
Noise Signal
Combined Signal
Time
Amplitude
When SNR is very low, the probability of error is nearly 50%.
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15. Bit Error Rate
A measure of quality of communications is how many errors occur because of added “noise” relative to signal power
This is known as Bit Error Rate: it is an important metric in telecoms
Bit Error Rate (BER)
Signal to Noise Ratio (SNR) in dB
BER for a random noise communications system
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16. Business Aspects of Digital
Advantages:
Robustness against noise
Lower cost of signal processing and storage
Specially in the light of Moore’s law
Information systems integration between business and trade partners
Important to Information Systems Management
Disadvantages:
Lower quality (specially because of quantization error)
Requirement to protocols and standards
Significantly larger scope of standards
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17. Case Study: Integrated Service Digital Networks
The G.711 vocoder technology was used in the ISDN system
ISDN standards were one of the first systems in data communications
They emerged as computer communications grew in importance, and as fax devices became popular in mid to late 1980s
They were designed to enable transmission of voice signals and data signals over the same telephony lines: it even envisaged video telephony using the ISDN standards
The standards still used circuit switching: one telephone line would be occupied by a constant signal transmission
Two types of channels are defined in ISDN
B (bearer) channel for transmission of one unit of data: B is 64 kbps
D (delta) channel is used for sending control signals: D can be 16 or 64 kbps
Ordinary telephone lines were considered to carry 2B+D data rates (144 kbps)
Video telephony would use up to 30B rates (around 2 Mbps) over a special physical medium.
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18. ISDN Services
Soon it was realised that voice transmission did not require as much as 64 kbps
Furthermore, A/D and D/A converters were required in entire system (or costly converting gateways)
Furthermore, there was no market for data transmission
Few home PCs
No world wide web yet
No real need of data transmission outside the office
Commercial usage of ISDN standard had to wait until late 1990s for purely circuit-switched data communications
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19. Digital Voice: G.711* Voice Coder (Vocoder)
According to Nyquist rate, voice has to be sampled at twice the frequency rate of the signal.
300
3400
4000
Frequency (Hz)
Voice Spectrum
Remember: voice signals have significant frequency components of up to 4 KHz. This means sampling rate must be set at more than 8000 samples/sec.
Further, 256 = 28 sampling levels are used to represent sample values. This can be represented by an 8-bit word
This means initially voice was digitised at a 64 kilobits/sec rate.
This is an inefficient way of source coding, but renders a very high voice quality.
Analogue to Digital (A/D) Converter
*G.711 is an ITU-T standard for audio coding, but it is primarily used in telephony. The standard was released for usage in 1972.
64 kbps digital stream
4 KHz voice stream
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20. Time and Frequency Domains
Once we stood beside the shore
A chink in the wall allowed a draft to blow
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21. Continuous Waveform 1 Second
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22. Unequal Quantization Levels
Since voice variations are much more in lower amplitudes, quantization levels are changed to give a more accurate conversion at these levels. 8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1
Amplitude
Time
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23. Differential Analog to Digital Conversion
Instead of quantizing the sample, the difference between two sample may be quantized
This removes the correlation between two samples, reducing the number of bits required per sample to 4 bits
The bit rate is then 8000 * 4 = 32,000 bps. 8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1
Amplitude
Time
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24. Original Speech signal Perceptual Weighing Factor
Synthesis Coding
Another method of voice coding is to consider how voice is generated and then try to represent voice as its components
Our speech consists of a ‘buzzer’ sound generated by the vibrating vocal cords, and hissing and popping sounds as air pass through stationary vocal cords and shaped by our tongue, lips and throat.
A set of frequencies and speech filters and code parameters can reproduce voice
Original Speech signal +
Codebook
Speech Filters -
To next code word
Calculate Error
Perceptual Weighing Factor
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25. Lossy Voice Coders
One synthesis coding method is referred to Code Excited Linear Predictive (CELP)
A number of vocoders have been designed using CELP.
CELP is used in G.729 standard (VoIP systems) and in AMR which is used in GSM and 3G/4G mobile phones
G.729 encodes voice at 8 kbps (although some variations exist.)
AMR codecs rates are: 12.2, 10.2, 7.95, 7.40, 6.70, 5.90, 5.15 and 4.75 kbps.
A different class of AMR codecs are being standardised for “beyond” 3G systems. These are called AMR Wideband (AMR-WB). These have better quality (use a 7 kHz filtered voice) and necessarily higher rates: 23.85, 23.05, 19.85, 18.25, 15.85, 14.25, 12.65, 8.85 and 6.60 kbps.
Used in Voice over LTE systems (also 3G systems)
CELP follows a source-filter model of speech prediction.
The source-filter model of speech production assumes that the vocal cords are the source of spectrally flat sound (the excitation signal), and that the vocal tract acts as a filter to spectrally shape the various sounds of speech. While still an approximation, the model is widely used in speech coding because of its simplicity. Its use is also the reason why most speech codecs (Speex included) perform badly on music signals. The different phonemes can be distinguished by their excitation (source) and spectral shape (filter). Voiced sounds (e.g. vowels) have an excitation signal that is periodic and that can be approximated by an impulse train in the time domain or by regularly-spaced harmonics in the frequency domain. On the other hand, fricatives (such as the "s", "sh" and "f" sounds) have an excitation signal that is similar to white Gaussian noise. So called voice fricatives (such as "z" and "v") have excitation signal composed of an harmonic part and a noisy part. (Source Further information is available from
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26. Perceptual Quality Comparison
Different coding techniques are compared using perceptual metrics
One such metric is called Mean Opinion Score (MOS)
NB-AMR
WB-AMR
Rate (kbps)
MOS
4.75
2.8
6.60
3.2
6.70
3.1
8.85
3.5
7.40
12.65
4.0
10.20
3.3
15.85
4.1
12.20
3.4
18.25
4.2
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27. Case Study: Skype Popularised VoIP services
Ease of use and high perceptual quality
Active at the service/content layer
Content and Services Layer
Connectivity Retail Layer
Subscriber / End user
Infrastructure Layer
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28. Audio Source Coding
Compact disk standard development began by Sony and Philips in the late 1970s.
In CDs, an analogue audio source is converted to a digital stream using Pulse Coded-Modulation (PCM) technique.
For Audio, the waveform is sampled at the Nyquist rate, 44.1 kHz, and converted to a digital stream at a quantization of 216 levels (=65536 levels).
This is a very inefficient method of encoding as it does not take into consideration:
The characteristics of audio signals
Our auditory capabilities (how sensitive are our ears? What can they perceive?) 8 7 6 5 4 3 2 1 -8 -7 -6 -5 -4 -3 -2 -1
Time
Amplitude
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29. MPEG and MP3
Digital Audio and Video compression work started in the 1980s, primarily through a European Community project Eureka.
The Moving Picture Experts Group (MPEG) was formed to develop standards for Digital Audio Broadcasting (DAB) and Digital Video Broadcasting (DVB)
Several technologies have been realized through this work
MPEG-1, a digital Audio and Video source encoding technique, used in Video CDs.
MPEG-2, a digital video source coding, used in Digital Video Discs (DVDs)
MPEG-4, a digital video source coding used in High Definition (HD) DVDs and Blu-Ray disks.
MP3 standard was developed initially as part of the MPEG-1 standard.
It takes advantage of how we human perceive sound
Discard perceptually insignificant information
Remove redundancies in the audio signal
For example stereo sound can not be distinguished at lower frequencies
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30. Lossy Digital Audio Standards
A number of audio encoding standards exist
Many of them are proprietary
Windows Media Player
Real Audio
iTune AAC
MP3
As MP3 was developed by a consortium of universities and companies, it has the lowest patent barrier
And therefore used most widely
iTune uses a technology called Advanced Audio Coding (AAC)
This technology is associated with the MPEG-2 and MPEG-4 standards, and is principally the same as MP3, but there are some advances, which yield better quality at lower bit rates
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31. Case Study: iTunes
Popularised MP3 technology through creation of a full platform
Created a system whereby music could be created and purchased
Content and Services Layer
Connectivity Retail Layer
Subscriber / End user
Infrastructure Layer
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32. Video Coding A video signal contains much more information than audio
A picture is worth a thousand words!
To encode video, one must decompose a picture into a set of data pixels, which can each then be digitised, and converted into a sequence of binary data
The data is then digitized, frame-by-frame at a suitable rate (25~30 frame per second.)
Broadcast analogue TV uses 6-8 MHz of bandwidth.
Using a similar digital encoding as PCM with a 224 quantisation range will lead to:
8*2*24 Mbit/sec = 384 Mbps
A DVD capacity is 4.5 giga-Bytes, and can provide storage for 94 seconds of such digital information
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33. Image Coding An image is made of pixels Which are correlated
Therefore, information theory can be used to compress data to its entropy without any loss
This is done by coding techniques such GIF or PNG
There are also lossy techniques
For example the JPEG standard (JPG)
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34. Discrete Cosine Transform (DCT)
In video also, the information content is much smaller
Efficient source encoders take advantage of this to digitize video
A digital picture may be uniquely defined in spatial (time) domain as a matrix of pixels, each with a certain colour and luminance. The picture may be equally represented in the frequency domain, where the information on the changes between pixels colour and luminance are given.
The conversion process between Time and Frequency domains uses transform techniques called DCT, and inverse DCT (IDCT)
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35. Some DCT Examples Time Domain Frequency Domain
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36. JPEG Variability
JPEG pictures can therefore be encoded with different sizes, with a designed loss
They can be adapted to the medium where they are transported
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37. Video Coding: MPEG-2 Standard
MPEG-2 standard is used in the DVD standards and compresses data based on the DCT technology and temporal (inter-frame) differential coding
Three kinds of frames are specified: intra-coded frames (I-frames), predictive-coded frames (P-frames), and bi-directionally-predictive-coded frames (B-frames).
I-Frames are independent of previous or following frames. They independently digitally encode a video frame.
P-frames provide more compression as they take advantage of I-Frames
B-Frames depend on P- and I-Frames, and can be highly compressed.
A typical sequence may be like: IBBPBBPBBPBBI I B B P B B P B B I B B P B B P B B I
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38. MPEG Standards
A number of MPEG standards have been developed for audio and video applications.
These standards have been instrumental in facilitating video conferencing, digital TV, video telephony and video streaming application.
A list of main standards and their application are shown here:
Codec
Standard
Applications
MPEG-1
H.261
Video CD Digital Audio Broadcasting (DAB)
MPEG-2
H.262
DVD, Blu-Ray DVD Digital Video Broadcasting (DVB)
MPEG-4
H.264
Blu-Ray DVD Video Streaming (YouTube, Vimeo, Etc.)
Video telephony (e.g. FaceTime) HDTV Broadcasting XAVC (4K)
MPEG-H
H.265
High Efficiency Video Coding 8K Ultra High Definition TV
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