Chapter 5 Analogue to Digital Signal Sampling Miners patent on sampling commutator Lukes narrative of theoretical development Rule of thumb development and acceptance Theoretical formulation ID: 633943
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Riaz Esmailzadehriazesma@andrew.cmu.edu
Chapter 5
Analogue
to DigitalSlide2
Signal Sampling Miner’s patent on sampling commutator Luke’s narrative of theoretical development
Rule of thumb development and acceptance
Theoretical formulation
Mathematical discovery
Broadband Telecommunications Technologies and Management
© 2016, Riaz Esmailzadeh
2Slide3
Analog SignalsNatural phenomena are continuous waveformsSeismometer
Temperature
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3Slide4
Discrete RepresentationTemperature 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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4Slide5
ExampleWhat is the frequency of this signalWhich of the discrete representation is more accurate?
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5
Amplitude
Time
Time
Amplitude
Time
Amplitude
Time
Amplitude
(B)
(A)
(C)
(D)
1 s
1 s
1
-1
1
-1
1
-1
1
-1
1 s
1 sSlide6
Nyquist TheoremThe 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.
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6
Amplitude
Time
Time
Amplitude
(A)
(B)
1 s
1
-1
1
-1
1 sSlide7
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 {0.913410317, 0.662541770, 0.137126512, -0.543347179, -0.980775131, -0.398801013, 0.823661318, 0.286615541, -0.917042669, 0.995046175
}Or by: {0.913, 0.663, 0.137, -0.543, -0.981, -0.399, 0.824, 0.287, -0.917, 0.995
}
Which of these two
representations is more
efficient?
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Time
Amplitude
(B)
1
-1
1 sSlide8
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
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8
Time
Amplitude
Time
Amplitude
(A)
(B)
1 s
1
-1
1
-1
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000Slide9
Quantization Error and Number of BitsIf the number of quantization levels is not large enough, then there will be quantization errorsHere 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 bitsRequired accuracyDevice structure and
telecommunicationsprotocol. Usually as a multiple
of 8 bits or 1 byteBroadband Telecommunications Technologies and Management
© 2016, Riaz Esmailzadeh
9
Time
Amplitude
(B)
1
-1
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000Slide10
Why Digital?Analogue transmission of signals is degraded by the presence of noise in the network
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10
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
Electronics
Exchange
Noise
S
Exchange
Noise
S
Noise
SSlide11
Noise AccumulationAn 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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11Slide12
Digital Signals and NoiseConsider the following digitals signals and the effect of noise on it
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This digital signal may be detected without error at a receiver and perfectly reproduced. Here SNR ≈ 10.
1
1
1
1
-1
-1
-1
-1
-1
Digital
Stream
Noise
Signal
Combined Signal
Time
AmplitudeSlide13
Errors (SNR = 0.5)Consider the following signal when noise is relatively increased
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When noise level is high, then some bits may be received in error.
1
1
1
1
-1
-1
-1
-1
-1
Digital
Stream
Noise
Signal
Combined Signal
Time
AmplitudeSlide14
Larger Noise and more Errors (SNR = 0.1)Consider the following digitals signals and the effect of noise on it
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When SNR is very low, the probability of error is nearly 50%.
1
1
1
1
-1
-1
-1
-1
-1
Digital
Stream
Noise
Signal
Combined Signal
Time
AmplitudeSlide15
Bit Error RateA measure of quality of communications is how many errors occur because of added “noise” relative to signal powerThis is known as Bit Error Rate: it is an important metric in telecoms
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Bit Error Rate (BER)
Signal to Noise Ratio (SNR) in dB
BER for a random noise communications systemSlide16
Business Aspects of DigitalAdvantages: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
partnersImportant to Information Systems ManagementDisadvantages:
Lower quality (specially because of quantization error)Requirement to protocols and standardsSignificantly larger scope of standards
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16Slide17
Case Study: Integrated Service Digital NetworksThe 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 1980sThey 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
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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.Slide18
ISDN ServicesSoon 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 officeCommercial usage of ISDN standard
had to wait until late 1990s for purely circuit-switched data communications
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18Slide19
Digital Voice: G.711* Voice Coder (Vocoder)According to Nyquist rate, voice has to be sampled at twice the frequency rate of the signal.
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Analogue
to Digital
(A/D)
Converter
4 KHz
voice stream
64 kbps
digital stream
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 = 2
8
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.
0
300
3400
4000
Frequency (Hz)
Voice Spectrum
*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.Slide20
Time and Frequency Domains
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Once we stood beside the shore
A chink in the wall allowed a draft to blowSlide21
1 Second
Continuous Waveform
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21Slide22
Unequal Quantization LevelsSince voice variations are much more in lower amplitudes, quantization levels are changed to give a more accurate conversion at these levels.
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8
7
6
5
4
3
2
1
0
-8
-7
-6
-5
-4
-3
-2
-1
Amplitude
TimeSlide23
Differential Analog to Digital Conversion Instead of quantizing the sample, the difference between two sample may be quantizedThis 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.
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8
7
6
5
4
3
2
1
0
-8
-7
-6
-5
-4
-3
-2
-1
Amplitude
TimeSlide24
Synthesis CodingAnother 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
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Codebook
Speech
Filters
Perceptual
Weighing
Factor
Calculate
Error
To next code word
Original
Speech
signal
-
+Slide25
Lossy Voice CodersOne 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
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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) Slide26
Perceptual Quality Comparison Different coding techniques are compared using perceptual metricsOne such metric is called Mean Opinion Score (MOS)
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NB-AMR
WB-AMR
Rate (kbps)
MOS
Rate (kbps)
MOS
4.75
2.8
6.60
3.2
6.70
3.1
8.85
3.5
7.40
3.2
12.65
4.0
10.20
3.3
15.85
4.1
12.20
3.4
18.25
4.2Slide27
Case Study: SkypePopularised VoIP servicesEase of use and high
perceptual quality
Active at the service/content layer
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Content and Services Layer
Connectivity Retail Layer
Subscriber / End user
Infrastructure LayerSlide28
Audio Source CodingCompact 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
2
16 levels (=65536 levels).
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8
7
6
5
4
3
2
1
0
-8
-7
-6
-5
-4
-3
-2
-1
Time
Amplitude
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?)Slide29
MPEG and MP3Digital 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 soundDiscard perceptually insignificant information
Remove redundancies in the audio signal
For example stereo sound can not be distinguished at lower frequencies
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29Slide30
Lossy Digital Audio StandardsA number of audio encoding standards exist
Many of them are proprietary
Windows Media Player
Real Audio
iTune AACMP3
As MP3 was developed by a consortium of universities and companies, it has the lowest patent barrierAnd 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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30Slide31
Case Study: iTunesPopularised MP3 technology through creation of a full platform
Created a system whereby music could be
created and purchased
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Content and Services Layer
Connectivity Retail Layer
Subscriber / End user
Infrastructure LayerSlide32
Video CodingA 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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32Slide33
Image Coding An image is made of pixelsWhich are correlated
Therefore, information theory can be
used to compress data to its
entropy without any loss
This is done by coding techniques suchGIF or PNG There are also lossy techniques
For example the JPEG standard (JPG)
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33Slide34
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.
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The conversion process between Time and Frequency domains uses transform techniques called DCT, and inverse DCT (IDCT)Slide35
Some DCT Examples
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Time Domain
Frequency DomainSlide36
JPEG VariabilityJPEG pictures can therefore be encoded with different sizes, with a designed lossThey can be adapted to the medium where they are transported
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36Slide37
Video Coding: MPEG-2 StandardMPEG-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
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I
B
B
P
B
B
P
B
B
I
B
B
P
B
B
P
B
B
ISlide38
MPEG StandardsA 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:Broadband Telecommunications Technologies and Management
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38
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