waveform coding techniques

1

Advanced Digital Communication

Waveform Coding Techniques

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Waveform Coding Techniques Pulse-code modulation Channel Noise and Error probability Quantization Noise and Signal to Noise

Ratio Robust Quantization Differential Pulse Code Modulation Delta Modulation Coding Speech at Low Bit Rates Applications

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Signal Encoding - 4 Types

Information Digital Analog

Signal Digital Analog

Digital data, digital signalTwo different voltage levels for binary 0 &1.More complex encoding schemes are used to to improve performance, by altering the spectrum of the signal and providing synchronization

capability

Digital data, Analog signalModem converts digital data into analog signal so that it can be transmitted over an analog line.

ASK, FSK, PSK Performance QAM

Analog data, digital signal

Voice & Video

PCMDM

Performance

Analog data, Analog signal

AM, FM, PM

Digital Analog

Digital

Analog

DATA

SIGNAL

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Taxonomy of Speech CodersSpeech Coders

Waveform Coders Source Coders

Time Domain: PCM, ADPCM

Frequency Domain: e.g. Sub-band coder,Adaptive transform coder

Linear Predictive Coder

Vocoder

Waveform coders: attempts to preserve the signal waveform not speech specific (I.e. general A-to-D conv)

PCM 64 kbps, ADPCM 32 kpbs, CVSDM 32 kbpsVocoders:

Analyse speech, extract and transmit model parameters Use model parameters to synthesize speech LPC-10: 2.4 kbps

Hybrids: Combine best of both… Eg: CELP (used in GSM)

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From analog signal to digital code (PCM)

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Digital representation of Analog signals Advantages

ruggedness to transmission noise and interference

efficient regeneration of the coded signal along the transmission path

the potential for communication privacy and security through encryption

the possibility of a uniform format for different kinds of baseband signals

Disadvantageous Increased transmission bandwidth

requirement Increased system complexity

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PCM PCM belongs to a class of signal

coders known as waveform coders in which an analog signal is approximated by mimicking the amplitude vs time waveform and hence the name

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What is meant by PCM? Pulse code modulation (PCM) is a

method of signal coding in which the message signal is sampled, the amplitude of each sample is rounded off to the nearest one of a finite set of discrete levels and encoded so that both time and amplitude are represented in discrete form.. This allows the message to be transmitted by means of a digital waveform.

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A/D

D/A

PCM system : basic elements

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Basic Signal Processing Operations in PCM

Sampling Quantizing Encoding Regeneration Decoding Reconstruction Multiplexing Synchronization

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Sampling The incoming message wave is sampled with

a train of narrow rectangular pulses so as to closely approximate the sampling process

To ensure perfect reconstruction of message the sampling rate must be greater than twice the highest frequency component W of the message wave

In practice a low pass pre-alias filter is used to at the front of the sampler to exclude frequencies greater than W before sampling

The application of sampling permits the reduction of the continuously varying message wave to a limited number of discrete values per second

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Sampling an analogue signal

Prior to digitisation, signals must be sampled With a frequency fs=2B=1/T

ADC converts the height of each pulse into binary representation

Sampling involves the multiplication of the signal by a train of sampling pulses

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Sampling as multiplication by a sampling waveform:

Sampling pulse is short enough so that can normally considered have zero duration

DAC, however produces pulses length T

Multiplication = Amplitude modulation Amplitude modulation produces sidebands…

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The conversion of an analog (continuous ) sample of the signal into digital (discrete) form is called quantizing process

human ear / eye can detect only finite intensity differences

it is not necessary to transmit the exact amplitude of samples

original analog signal may be approximated by a signal constructed of discrete amplitudes

Quantizing

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Quantizing Reduce the number of distinct output

values to a much smaller set. Main source of the “loss" in lossy

compression. Three different forms of quantization.

Uniform: midrise and midtread quantizers.

Nonuniform: companded quantizer. Vector Quantization.

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Quantized signal

each value is translated to its 7-bit binary equivalent the 8th bit indicates sign

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Quantized signal

first three sample values

← ← ←

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Basic signal – processing operations in PCM

Quantization

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The peak-to-peak range of input sample values is subdivided into a finite set of decision levels or decision thresholds that are aligned with the “risers” of the staircase

The output is assigned a discrete value selected from a finite set of representation levels or reconstruction values that are aligned with the treads of the stair case

Quantizing

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midtread midrise

-Δ

Δ

2Δ

3Δ

-2Δ

-3Δ

3Δ/2

Δ/2

5Δ/2

....... ↑ 7Δ/2overload

level

Δ/2

3Δ/2

5Δ/2

7Δ/2

Δ 2Δ 3Δ 4Δ

overloadlevel

decisionthresholds

representationlevels

representationlevels

Two types of quantization

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M = EvenZero is not one of the output levelsZero is a decision boundary

M = OddZero is one of the output levelsZero is reconstruction level

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Symmetric uniform quantization midtread

peak-to-peak range of input sample values is sub-divided into a finite set of decision levels or decision thresholds

thresholds are aligned with risers decision thresholds are located at ±

Δ/2, ± 3Δ/2, …. output is assigned a discrete value

aligned with the tread of the staircase steps are at 0, ± Δ, ± 2Δ, …..

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Symmetric uniform quantization : midrise

decision thresholds are located at 0, ± Δ, ± 2Δ, …..

representation levels are at ± Δ/2, ± 3Δ/2, ± 5Δ/2, ….

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Symmetric uniform quantization Overload level :

the absolute value of which is 0.5 times peak-to-peak range of input sample values

Quantization error : the difference between values of output

and input of the quantizer Max. instantaneous value = 0.5 step

size total range of variation is

– (0.5 step) to + (0.5 step)

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Encoding A process to translate the discrete set of

sample values to a more appropriate form of signal best suited for transmission over a line, radio path or optical fibre

One of the discrete events in a code is called a code element or a symbol

A particular arrangement of symbols used in a code to represent a single value of a discrete set is called a code word or character

In a binary code, each symbol may be either of two distinct values or kinds such as the presence or absence of a pulse.

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Regenerative Repeater

Regeneration

To control the effect of noise and distortion while passing through a channel

Three functions of the regenerative repeater equalizing, timing and decision making

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Regeneration Equalizer :

shapes the received pulses to compensate for the impairment in amplitude and phase

timing circuit : provides periodic clock pulses for sampling

the received & equalized pulses decision making device :

at each bit interval, makes a decision whether a pulse is present (exceeds a predetermined voltage level) or not ; accordingly transmits a new pulse (1 or 0)

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Regeneration Departure of regenerated signal

The presence of channel noise and interference causes the repeater to make wrong decisions occasionally

Wrong decision : bit error Spacing between pulses deviates

from its assigned value causes jitter in to the regenerated pulse position, there by causing distortion

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Decoding The receiver reshapes and

cleans up the received pulses These clean pulses are

regrouped into code words and decoded or mapped back into a PAM signal

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Reconstruction Decoder output is passed

through a low-pass reconstruction filter whose cut off frequency = message bandwidth

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Multiplexing Different message sources are

multiplexed by time division

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Synchronization Timing operations at the receiver

must follow closely the corresponding operations at the transmitter

a local clock at the receiver to keep the same time as the distant transmitter clock

synchronization pulse or frame is transmitted alongwith code elements

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Channel Noise and Error probability

Performance of PCM system is influenced by Channel Noise, which may be

introduced any where along the channel path

Quantizing noise, which is introduced in the transmitter and is carried along to the receiver output

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Channel Noise The effect of transmission noise is

to introduce transmission errors Symbol 0 occupationally mistaken

as 1 and vice versa The fidelity (reliability) of

information transmission by PCM in the presence of channel noise is measured in terms of error rate or probability of error

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Additive White Gaussian Noise A basic and generally accepted model for thermal noise

in communication channels, is the set of assumptions that

the noise is additive, i.e., the received signal equals the transmit signal plus some noise, where the noise is statistically independent of the signal.

the noise is white, i.e, the power spectral density is flat, so the autocorrelation of the noise in time domain is zero for any non-zero time offset.

the noise samples have a Gaussian distribution. Mostly it is also assumed that the channel is Linear and

Time Invariant. The most basic results further assume that it is also frequency non-selective.

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The Basic SNR Parameter for Digital Communication Systems• In digital communications, we more often

use Eb/N0, a normalized version of SNR, as a figure of merit.

R

W

N

S

WN

RS

WN

ST

N

E bbb

/

/

/0

Eb = bit energy, S = signal power

Tb = bit time, Rb = R = bit rate

N0 = noise power spectral density

N = noise power, W = bandwidth

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Nonuniform quantizationRobust quantization

As in speech transmission, the same quantizer has to accommodate input signals with widely varying power levels.

A nonuniform quantizer for which the SNR remains constant over a wide range of input power levels is called robust

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What you mean by non-uniform quantization?

Step size is not uniform. Non uniform quantizer is characterized by a step size that increases as the separation from the origin of the transfer characteristics is increased. Non-uniform quantization is otherwise called as robust quantization

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Nonuniform quantization In the case of uniform quantization levels, the

quantization noise power depends only on the spacing between the levels, and is independent of the actual signal level at any instant.

The SNR decreases with a decrease in the input power level relative to the maximum range of the quantizer, which is undesirable in many applications.

For example, in a speech system a fixed quantization noise power will be more objectionable when a quiet speaker is speaking than when a loud one is.

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Nonuniform quantization In A remedy is to use nonuniform quantization levels.

This can be achieved by using a nonuniform quantizer

level 7

level 6

level 5

level 4 level 3

level 2

level 1

level 0

0

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Nonuniform quantizationRobust quantization

As in speech transmission, the same quantizer has to accommodate input signals with widely varying power levels.

A nonuniform quantizer for which the SNR remains constant over a wide range of input power levels is called robust.

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Nonuniform quantizationProbability density function A uniform quantizer makes sense

when the probability distribution of the signal in the range -Vmax to Vmax is uniform. If we have reason to believe that the distribution is nonuniform, and we know what the actual distribution is, then we can place nonuniform quantization levels in an optimal manner

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Nonuniform quantizationProbability density function Recall from the discussion on information theory that

the entropy is maximized if the probability of occurrence of each level is equal.

Therefore choose the quantization levels such that the probabilities of occurrence in each level are equal.

p(x)

0x

a b c d 1

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More often, nonuniform quantization is achieved by first distorting the original signal with a nonlinear compressor characteristic, and then using a uniform quantizer on the result: input

output

a

2a

3a

4a

-4a

-3a

-2a

-aa 2a 3a 4a

-a-2a-3a-4a

Nonuniform levels

Uniform levels

Nonuniform quantizationCompanding

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Nonuniform quantizationCompanding A given signal change at small

magnitudes will then carry the uniform quantizer through more steps than the same change at large magnitudes. At the receiver, an inverse compression characteristic (or expansion) is applied, so that the overall transmission is not distorted. The processing pair (compression and expansion) is usually referred to as companding.

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Nonuniform quantization µ-law compander

The µ-law compander is characterized by

Vout = log(1+µVin) / log(1+µ)

The µ-law companding is used for PCM telephone systems in the USA, Canada and Japan, with the standard value of µ = 255

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1Vin

Vou

t

mu=255

mu=1

mu=10

mu=100

mu=1000

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The A-law compander is characterized by

Vout = A*Vin / {1+log(A)}

for Vin < 1/A Vout = A*{1+log(A*Vin)

/ {1+log(A)} for 1/A ≤ Vin The A-law companding

is used for PCM telephone systems in Europe, with A = 87.56

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1Vin

Vou

t

A=1

A=10

A=100

A=1000

A=87.6

Nonuniform quantizationA-law compander

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Non-uniform quantization For a non-uniform

quantizer, the quantization error power is related to the quantizer’s input distribution, since it has smaller quantization step for small input and larger quantization step for large input.

In most cases the quantizer input has a distribution similar to Normal distribution, which means using a non-uniform quantizer will lead to smaller quantization error power.

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UNIFORM - QUANTIZER

Variance, Features: Variance is valid only if the

input signal does not overload Quantizer

SNR Decreases with a decrease in the input power level.

22

Q

Δσ =

12

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ROBUST QUANTIZER

A Quantizer whose SNR remains

essentially constant for a wide range

of input power levels.…. Non Uniform Quantizer

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Non Uniform Quantizer

Variable Step-Size. Smaller amplitude - Smaller

Step Size. Larger amplitude - Large

Step size

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Non- UniformQuantizer MODEL

CompressorUniform

QuantizerExpander

Input Output

Compander = Compressor + Expander

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Compressor

Compressor input

Com

pres

sor

out

put

60

Expander

Expander input

Exp

ande

r o

utpu

t

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Quantization Error-1

Transfer Characteristics Compressor --- C(x) Expander --- C-1(x)

C(x). C-1(x) = 1

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Quantization error-2

Compressor Characteristics ( for large L )

max

k

2xdc(x)= for k =0,1,.....L - 1

dx LΔ

Δk = Width in the interval Ik

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Let fX(x) = PDF of ‘X’ .

Assumptions: fX(x) is Symmetric fX(x) is approximately constant

in each interval. ie.. fX(x) = fX(yk)

64


fX(x) = fX(yk)

Δk = xk+1 - xk for k = 0, 1, … L-1.

pk = Probability of variable X

pk = P (xk < X < xk+1 ) = fX(x) Δk = fX(yk) Δk

L-1

kk=0

p = 1

65


Q = yk – X for xk < X < xk+1

Variance σQ

2 = E ( Q2) = E [( X – yk )2 ]

max

max

)()( 22x

x

XkQ dxxfyx

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1

21

0

2 )(k

k

x

x

kk

kL

kQ dxyx

p

Carrying out Integration w.r.t x

1

0

22

12

1 L

kkkQ p

( Δk2 / 12 ) - Variance of error in the Interval Ik

Δk = Δ for all k in Uniform Quantizer.

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Types of Companding

1. µ - law ( US, Canada & Japan)

2. A - law ( Europe)

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μ-law

=255 reduces noise power in speech ~20dB

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μ-law companding

10)1ln(

)/1ln()(

max

max

max

x

xxx

x

xc

μ = 255 - practical value

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A-law

A=1

A=100

A=2

Normalized input

Nor

mal

ized

out

put

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A-law

max

max

A x /x x 10£ £

1+lnA x A

max

max

1+ln(A x /x ) x1£ £ 1

1+lnA A x

max

)(

x

xc

Practical value for A = 87.5

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Companding Gain - Gc

Companding gain

For μ-law

0)(

xasdx

xdcGc

)1ln(

)(

dx

xdcGc

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Advantages ofNon Uniform Quantizer

Reduced Quantization noise High average SNR

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A

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B

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DPCM - Transmitter

^

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DPCM - Receiver

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Vocoder





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Voice Compression Technologies

Bandwidth(Kbps)

Quality

UnacceptableUnacceptable BusinessQuality

BusinessQuality

TollQuality

TollQuality

8

16

32

24

64

0

*PCM (G.711)

*PCM (G.711)

*ADPCM 32 (G.726)

*ADPCM 32 (G.726)

*ADPCM 24 (G.726)

*ADPCM 24 (G.726)

*ADPCM 16 (G.726)

*ADPCM 16 (G.726) *

LDCELP 16 (G.728)*

LDCELP 16 (G.728)

*CS-ACELP 8 (G.729)

*CS-ACELP 8 (G.729)*

LPC 4.8*

LPC 4.8

(Cellular)(Cellular)

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Bandwidth RequirementsVoice Band Traffic

Encoding/Encoding/CompressionCompression

ResultResultBit RateBit Rate

G.711 PCMG.711 PCMA-Law/A-Law/uu-Law-Law

64 kbps (DS0)64 kbps (DS0)

G.726 ADPCMG.726 ADPCM 16, 24, 32, 40 kbps16, 24, 32, 40 kbps

G.729 CS-ACELPG.729 CS-ACELP 8 kbps8 kbps

G.728 LD-CELPG.728 LD-CELP 16 kbps16 kbps

G.723.1 CELPG.723.1 CELP 6.3/5.3 kbps6.3/5.3 kbpsVariableVariable

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Voice Compression—ADPCM

Adaptive Differential Pulse Code Modulation Waveform coding scheme Adaptive: automatic companding Differential: encode the changes between samples only Rates and bits per sample:

32Kbps = 8 Kbps x 4 bits/sample24 Kbps = 8 Kbps x 3 bits/sample16 Kbps = 8 Kbps x 2 bits/sample

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Speech Coding Schemes [1],[2]Speech Coding Schemes

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Main Attributes of Speech Coders Bit rate - This is the number of bits per second (bps) which is

required to encode the speech into a data stream. Subjective quality This is the perceived quality of the

reconstructed speech at the receiver. It may not necessarily correlate to objective measures such as the signal-to-noise ratio. Subjective quality may be further subdivided into intelligibility and naturalness. The former refers to the ability of the spoken word to be understood; the latter refers to the “human-like" rather than “robotic" or “metallic“ characteristic of many current low-rate coders.

Complexity -The computational complexity is still an issue despite the availability of ever-increasing processing power. Invariably, coders which are able to reduce the bit rate require greater algorithmic complexity - often by several orders of magnitude.

Memory - The memory storage requirements are also related to the algorithmic complexity. Template-based coders require large amounts of fast memory to store algorithm coefficients and waveform prototypes.

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Main Attributes of Speech Coders Delay - Some processing delay is inevitable in a speech

coder. This is due not only to the algorithmic complexity (and hence computation time) but also to the buffering requirements of the algorithm. For real-time speech coders, the coding delay must be minimized in order to achieve acceptable levels of performance.

Error sensitivity - High-complexity coders, which are able to leverage more complex algorithms to achieve lower bit rates, often produce bit streams which are more susceptible to channel or storage errors. This may manifest itself in the form of noise bursts or other artifacts.

Bandwidth - refers to the frequency range which the coder is able to faithfully reproduce. Telephony applications are usually able to accept a lower bandwidth, with the possibility of compromising the speech intelligibility.

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A PCM technique that codes the difference between sample points to compress the digital data

more efficient because audio waves propagate in predictable patterns, DPCM predicts the next sample and codes the difference between the prediction and the actual point

Since differences between samples are expected to be smaller than the actual sampled amplitudes, fewer bits are required to represent the differences

Differential PCM

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DPCM Foe example if X(k) extends over the

interval VH-VL and using PCM X(k) is encoded using 28 =256 the the step size S = (VH-VL) / 28, that is VH-VL =256*S

If, However, the difference signal X(k)-X(k-1) extends only over +/- 2S the the quantized levels needed are +/- 0.5 S and at +/- 1.5 S. There are only 4 levels and two bits are adequate

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DPCM takes advantage of the high correlation between samples by encoding the difference between samples rather than the absolute sample value

Can reduce bit rate (by about 25 %) by using prediction based on previous samples

Sends only the difference between predicted and actual - 4 bits per sample

Over time, the error between the decoded signal and the differentially encoded signal increase …. so, periodically, a full pulse is sent rather than the difference

Differential PCM

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Differential PCM An extension of pulse code modulation which

differentially encodes the data to increase transmission efficiency

Differential PCM (DPCM) is used in many image and video compression algorithms, including JPEG.

The principle behind differential pulse code modulation is that the source data is likely to be an analogue signal, which is likely to change in amplitude quite gradually; there are unlikely to be any large jumps in amplitude over a short time. Therefore, the signal can be efficiently represented by an initial value, and incremental deltas against this value thereafter. Since these differences are likely to be small, fewer bits may be used to encode such a signal, and therefore throughput may be increased.

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Differential PCMFor the given input signal the sampled values are 1, 2, 4, 5, 6, 9, 7, 4, 3, 0, 2, 3, 5, 6. Encoded using standard pulse code modulation, this data set would require ceil(log2(9))1 = 4 bits per sample.

Notice, however, that the delta between two samples is never less than -3 or greater than +3. This gives a range of 7 values, which can be encoded in ceil(log2(7))1 = 3 bits per sample. If the encoding scheme used was differential pulse code modulation, the output would be:

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Differential PCM At the time of the PCM process, the differences

between input sample signals are minimal. Differential PCM (DPCM) is designed to calculate this difference and then transmit this small difference signal instead of the entire input sample signal. Since the difference between input samples is less than an entire input sample, the number of bits required for transmission is reduced. This allows for a reduction in the throughput required to transmit voice signals. Using DPCM can reduce the bit rate of voice transmission down to 48 kbps.

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Differential PCM : process 1. Input signal is sampled at a

constant sampling frequency (twice the input frequency)

2. Samples are modulated using the PAM process. At this point, the DPCM process takes over

3. Sampled input signal is stored in what is called a predictor

4. Predictor takes the stored sample signal and sends it through a differentiator

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Differential PCM : process 5. Differentiator compares the

previous sample signal with the current sample signal and sends this difference to the quantizing and coding phase of PCM

6. After quantizing and coding, the difference signal is transmitted to its final destination

7. At the receiving end of the network, everything is reversed

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Differential PCM : process 8. First the difference signal is

de - quantized 9. Then this difference signal

is added to a sample signal stored in a predictor

10. Resulting signal is sent to a low-pass filter that reconstructs the original input signal

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Differential PCM System

Transmitter

Receiver

xi(nTs)e(nTs)

predicted value xp(nTs)

v(nTs)

u(nTs) = xi(nTs) + q(nTs)

b(nTs)e(nTs) = xi(nTs) - xp(nTs)

predictionerror

Q(.)

_________

Reconstructionb(nTs)

Previous sample

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Differential PCM System

Baseband signal x(t) is sampled @ fs = 1 / Ts

to produce a sequence of correlated samples Ts seconds apart, denoted by {x(nTs)}

Quantizer Input e(nTs) = xi(nTs) - xp(nTs) where xi(nTs) is the unquantized sample xp(nTs) is its predicted value produced by a

predictor e(nTs) is called the prediction error, the amount

by which the predictor fails to predict the input correctly

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Differential PCM Let the quantizer input - output

characteristics be defined by the nonlinear function Q(.)

Quantizer output v(nTs) = Q {e(nTs)} = e(nTs) + q(nTs) where q(nTs) is the quantization error

The quantizer output v(nTs) is added to the predicted value xp(nTs) to produce the predictor input

u(nTs) = xp(nTs) + v(nTs)

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Differential PCM

u(nTs) = xp(nTs) + e(nTs) + q(nTs) = xi(nTs) + q(nTs)

Irrespective of the properties of the predictor, the quantized signal u(nTs) differs from the original input signal by the quantization error

Output at the receiver, differs from the original input only by the quantization error incurred as a result of quantizing the prediction error

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Output signal-to-quantization ratio is defined as

(SNR)O = σx2 / σQ

2 where σx

2 is the variance of the original input signal σQ

2 is the variance of the quantization error We can rewrite (SNR)O = (σx

2 / σE2) x (σE

2 / σQ2)

= GP x (SNR)P

where GP is the prediction gain produced by the differential quantization scheme

Differential PCM

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Delta Modulation is the one bit ( or two level) version of (DPCM) differential pulse code modulation.

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Delta Modulation The analog signal is approximated with

a series of segments Each segment of the approximated

signal is compared to the original analog wave to determine the increase or decrease in relative amplitude

The decision process for establishing the state of successive bits is determined by this comparison

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Delta Modulation only the change of information is

sent, i.e., only an increase or decrease of the signal amplitude from the previous sample is sent, whereas a no-change condition causes the modulated signal to remain at the same 0 or 1 state of the previous sample unique features : a one-bit codeword for the output

eliminates the need for word-framing simple design of transmitter and receiver

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Delta Modulation

δ

u(t)

signal xi(t) xi(t)

sampling period

u(t)

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Delta Modulation

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Delta Modulation

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Delta Modulation the difference between the input and

the approximation is quantized into only two levels, +δ or -δ

if the approximation falls below (above) the signal at the beginning of sampling period, it is increased (decreased) by δ

if the signal variation is not too rapid between successive samples, the staircase approximation is within ± δ

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Delta Modulation the step size Δ of the quantizer is given by Δ = 2δ prediction error e(nTs) = xi(nTs) – xp(nTs) = xi(nTs) – u(nTs - Ts)

binary quantity b(nTs) = δ sgn[e(nTs)] is the algebraic sign of the error, except for the scaling factor δ

b(nTs) is the one-bit word transmitted by the DM system

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Delta Modulation

xi(nTs)e(nTs) b(nTs)

u(nTs)

xp(nTs)

delay Ts

delay Ts

DM Transmitter

DM Receiver

removes out-of-band quantization noise

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Delta Modulation Quantization Noise – DM systems are subject

to Two Types of quantization error Slope overload distortion Granular noise

Slope overload distortion: This type of distortion is due to the use of a step size delta that is too small to follow portions of the waveform that have a steep slope. It can be reduced by increasing the step size.

Granular noise: This results from using a step size that is too large too large in parts of the waveform having a small slope. Granular noise can be reduced by decreasing the step size.

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Delta Modulation - example

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Define adaptive delta modulation The performance of a delta modulator

can be improved significantly by making the step size of the modulator assume a time- varying form. In particular, during a steep segment of the input signal the step size is increased. Conversely, when the input signal is varying slowly, the step is reduced , In this way, the step size is adapting to the level of the signal. The resulting method is called adaptive delta modulation (ADM).

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Adaptive Delta Modulation improved performance over DM step size of the modulator is

varied step size is adapted to the input

signal level during a steep segment of input

signal, step size is increased when input signal is varying

slowly, step size is reduced

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Adaptive Delta Modulation

x(nTs)

delay Ts

logic for step sizecontrol

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Coding speech at low bit rates Standard PCM operates at 64 Kbps Conservation of bandwidth / low bit

rates needed to facilitate secure transmission over low-capacity radio channels

Speech can be coded at low bit rates without compromising on acceptable fidelity may be as low as 2 Kbps

However, increase in processing complexity / processing delays are associated with this

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Coding speech at low bit rates

Design philosophy for a waveform coder for speech at low bit rates : To remove redundancies from the

speech signal as far as possible To assign the available bits to code the

non-redundant parts in an efficient way Algorithms for redundancy removal

and bit assignment become increasingly complex as bit rate is reduced

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Thumb rule Computational complexity

(measured in terms of multiply-add operations) increases by an order of magnitude for every halving of bit rate in the 64 to 8 Kbps range

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Define ADPCM. It means adaptive differential pulse code

modulation, a combination of adaptive quantization and adaptive prediction. Adaptive quantization refers to a quantizer that operates with a time varying step size. The autocorrelation function and power spectral density of speech signals are time varying functions of the respective variables. Predictors for such input should be time varying. So adaptive predictors are used.

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Coding speech at low bit rates by ADPCM Adaptive Differential PCM (achieves 32

Kbps)a widely used variation of PCM codes the difference between sample

points like differential PCM (DPCM)but also dynamically switches the coding scale to compensate for variations in amplitude and frequency

uses an adaptive predictor for the differences between pulses

how does ADPCM adapt these quantization levels ?

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if the difference signal is low, ADPCM increases the size of the quantization levels

if the difference signal is high, ADPCM decreases the size of the quantization levels

ADPCM adapts the quantization level to the size of the input difference signal

this generates an SNR that is uniform throughout the dynamic range of the difference signal

Coding speech at low bit rates by ADPCM

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ADPCM is a digital coding scheme that uses: both adaptive quantization and adaptive prediction

adaptive quantization : estimating the variance of the input

signal continuously adaptive prediction :

estimating the input signal from the quantized difference signal

Coding speech at low bit rates by ADPCM

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Coding speech at low bit rates:Adaptive quantization quantizer operates with a time-varying

step size Δ(nTs), where Ts is the sampling period

step size Δ(nTs) is varied to match the variance σx

2 of the input signal x(nTs) σx(nTs) is the standard deviation, varies

with time σxe(nTs) is an estimate of the standard

deviation adaptive quantization estimates σx(nTs)

continuously

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Two methods Derive forward estimates of σx(nTs)

using the unquantized samples of x(nTs) AQF

Derive backward estimates of σx(nTs) using the quantized samples of x(nTs) AQB

Coding speech at low bit rates:Adaptive quantization

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AQF the samples of the speech signal, the

unquantized ones, are buffered the samples are released after the

estimate σxe(nTs) has been obtained since estimate is done on unquantized

samples : step size Δ(nTs) is independent of quantizing noise

more reliable than the quantized case


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AQF : this method requires transmission of level information (typically 5 to 6 bits per step size sample) to the remote decoder of the receiver overheads / processing delay

AQB avoids problems of level transmission, buffering, delay practically more popular compared to

AQF


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Coding speech at low bit ratesAQB

x(nTs)

uses the recent history of the quantizer output to extract information for computation of Δ(nTs)

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What is meant by forward and backward estimation? AQF: Adaptive quantization with forward

estimation. Unquantized samples of the input signal are used to derive the forward estimates.

AQB: Adaptive quantization with backward estimation. Samples of the quantizer output are used to derive the backward estimates.

APF: Adaptive prediction with forward estimation, in which unquantized samples of the input signal are used to derive the forward estimates of the predictor coefficients.

APB: Adaptive prediction with backward estimation, in which Samples of the quantizer output and the prediction error are used to derive estimates of the predictor coefficients.

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Coding speech at low bit rates:Adaptive prediction Two methods Derive forward estimates of

predictor coefficients using the unquantized samples of x(nTs) APF

Derive backward estimates of predictor coefficients using the quantized samples of x(nTs) APB

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Coding speech at low bit ratesAPF

Buffer and predictor coefficient Calculator

To Channel

↓↓↓

also transmitted over channel

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Coding speech at low bit ratesAPB

x(nTs)

xe(nTs)

u(nTs)

y(nTs)

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Subband Coding In sub-band coding (SBC), the speech signal is

filtered into a number of subbands and each subband is adaptively encoded. The number of bits used in the encoding process differs for each subband signal with bits assigned to quantizers according to a perceptual criteria.

By encoding each subband individually, the quantization noise is confined within its subband. The output bit streams from each encoder are multiplexed and transmitted.

At the receiver demultiplexing is performed, followed by decoding of each subband data signal. The sampled subband signals are then combined to yield the recovered speech.

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Subband Coding Note that down sampling of subband signals must occur

at the output of the subband filters to avoid over sampling. The down sampling ratio is given by the ratio of original speech bandwidth to subband bandwidth.

Conventional filters cannot be used for the production of subband signals because of the finite width of the band-pass transition bands. If the bandpass filters overlap in the frequency domain, subsampling causes aliasing which destroys the harmonic structure of voiced sounds and results in unpleasant perceptual effects. If the bandpass ¯filters don't overlap, the speech signal cannot be perfectly reconstructed because the gaps between the channels introduce an audible echo. Quadrature mirror ¯filter (QMF) banks [32] overcome this problem and enable perfect reconstruction of the speech signal.

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Adaptive Subband Coding It is a frequency domain coder, in

which the speech signal is divided in to number of subbands and each one is coded separately. It uses non masking phenomenon in perception for a better speech quality. The noise shaping is done by the adaptive bit assignment.

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Coding speech at low bit rates Adaptive Sub-band Coding (ASBC) PCM and ADPCM function in time-

domain ASBC is a frequency domain coder Speech signal is divided into a

number of sub-bands Each sub-band is encoded separately Capable of achieving 16 Kbps with

quality comparable to 64 Kbps PCM

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Uses the following characteristics of speech and hearing mechanism to advantage : quasi-periodic nature of voiced speech noise-masking of hearing mechanism

Quasi-periodic nature People speak with a characteristic pitch frequency This permits reliable prediction of pitch, reduction in prediction error and reduction in number of bits per sample to be transmitted

Coding speech at low bit rates: (ASBC)

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Noise-masking phenomenon Human ear does not perceive in a frequency band if the noise is about 15 dB below the signal level in that band

A relatively large coding error can be tolerated near formants, coding rate can be reduced

A formant is a peak in an acoustic frequency spectrum which results from the resonant frequencies of any acoustical system. It is most commonly invoked in phonetics or acoustics involving the resonant frequencies of vocal tracts


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The number of bits used to encode each sub-band is varied dynamically, called adaptive bit assignment

The no. of bits is shared with other bands, as necessary, depending on the encoding accuracy to be achieved for each sub-band


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Examples : low frequency predominated signal

may use bit assignment 5, 2, 1, 0 high frequency predominated signal

may use bit assignment 1, 1, 3, sub-bands with little or no energy content

may not have to be encoded at all Quantizing noise within any sub-

band is limited to that sub-band ------ low-level speech of a sub-band cannot be hidden by quantizing noise of another sub-band


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Steps : 1. Speech band is divided into number of

contiguous bands using a filter-bank of (BPFs) band-pass filters (typically 4 to 8)

2. The output of each BPF is translated in frequency to a low-pass form by a modulation process

3. The sub-band signals are sampled at a rate slightly higher than the relevant Nyquist rate


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Steps : 4. The samples are digitally encoded

using ADPCM. Each sub-band is encoded based on the spectral content of that sub-band

5. The encoded samples are multiplexed and transmitted

6. Bit assignment info is also transmitted to enable the receiver decode them individually


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Steps : 7. The decoded sub-bands are

converted at the receiver to their original locations in the frequency band

8. The frequency re-translated sub-bands are summed up to produce a close replica of the original signal


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fs = sampling rate of original (full-band) signal

N = average number of bits used to encode a sample of the signal

M = number of sub-bands Bit rate = N x fs per second Nfs = (MN) x (fs / M) Bit rate = (Total no. of bits per sample)

x (Sampling rate per sub-band)


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Example : No. of sub-bands = M = 4 Sampling rate of original signal = fs

= 8 KHz Average no. of bits per sample = 2 Sampling rate for each sub-band =

2 KHz Total no. of bits per sample = 8


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Subjective quality : Mean Opinion Score (MOS)

In multimedia (audio, voice telephony, or video) especially when compression techniques are used ---

the MOS (more realistic than SNR) is used to provide a numerical indication of the perceived quality of received media after compression and/or transmission

An MOS is obtained by conducting formal tests on human subjects


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Subjective quality : Mean Opinion Score (MOS) the MOS is generated by averaging the

results of a set of standard subjective tests

a number of listeners rate the heard audio quality of test sentences read aloud by both male and female speakers over the communications medium being tested

the MOS is the arithmetic mean of all the individual scores

can range from 1 (worst) to 5 (best)


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Coding speech at low bit ratesSubjective quality : Mean Opinion Score (MOS)

MOS

Quality Impairment

5 Excellent / Perfect

Imperceptible

4 Good / High Perceptible, but not annoying

3 Fair / Communication

Slightly annoying

2 Poor Annoying

1 Bad Very annoying

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Subjective quality : Mean Opinion Score (MOS) Practical issues Using MOS ratings : 16 Kbps ASBC method

approaches ratings of 4, very close to the 64 Kbps and 32 Kbps DPCM methods

Using SNR ratings : 16 Kbps ASBC compares poorly with higher bit-rate PCM

ASBC falls short of 64 Kbps PCM and 32 Kbps ADPCM ---- quality drops sharply with tandem codings

however, not significant in an all-digital link


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Measuring Performance of Speech Coders

The quality of speech output of a speech coder is a function of bit-rate, complexity, delay and bandwidth.

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Digital Multiplexers Hierarchy of digital multiplexers,

whereby digitized voice, data, video signals are combined into one final data stream

Light wave transmission link That is well suited for use in long-

haul telecommunication network

Waveform Coding TechniquesApplications

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ApplicationsDigital Multiplexers

Waveform Coding Techniques

Computer outputsDigitized voiceDigitized faxTV signals

Operates at higher rates than inputs

at different rates

combining several digital signals at different rates into a single data stream at considerably higher bit rate than any of the inputs

Conceptual diagram of multiplexing-demultiplexing

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Accomplish multiplexing of digital signals by bit-by-bit interleaving procedure a selector switch that sequentially

selects a bit from each incoming line and then applies it to the high speed common line

at the receiver, the output from the common line is separated into low-speed individual components and delivered to respective destinations

Waveform coding techniques Applications-Digital Multiplexers

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Two major groups of digital multiplexers are used in practice

Low-speed operations Designed to combine relatively low speed digital signals

up to a maximum of 4800 bps, in to a higher speed multiplexed signal with a rate of up to 9600 bps

used primarily to transmit data over voice-grade channels

uses Modems for converting digital format to analog format

High-speed operations : Designed to operate at much higher bit rates, forms part

of data transmission service generally provided by communication carrier companies.

Example the T1 carrier system which has been developed by the BELL system in the United States in the early 1960s for digital voice communication over short-haul distances of 10-50 miles.


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Transmission Rates

64 kbits/s

Japanese Standard North AmericaStandard

European Standard

1544 kbits/s 2048 kbits/s

8448 kbits/s

34368 kbits/s

139264 kbits/s

564992 kbits/s

6312 kbits/s

44736 kbits/s

274176 kbits/s

32064 kbits/s

97728 kbits/s

97728 kbits/s

x24x30

x4x3

x4

x4

x3

x4

x5 x7

x6

x4

x4x3

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Digital Hierarchy

MULTIPLEXINGLEVELS(DS)

# OF VOICECHANNELS

NORTHAMERICA

EUROPE JAPAN

0 1 0.064 0.064 0.064

1 24 1.544 1.544

30 2.048

48 3.152 3.152

2(4xDS1)

96 6.312 6.312

120 8.448

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MultiplexingLevels

# OF VOICECHANNELS

NORTHAMERICA

EUROPE JAPAN

3 (7xDS2) 480 34.368 32.064

672 44.376

1344 91.053

1440 97.728

4 (6xDS3) 1920 139.264

4032 274.176

5760 397.200

7680 565.148

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Digital Hierarchy BELL System

T1 @ 1.544 mbpsT2 @ 6.312 mbpsT3 @ 44.736 mbpsT4 @ 274.176 mbps

MUX

PCM

MUX

DPCM

MUX

Digital Data

Channel Bank

T4

T3

T2

T1Voice Signals

12

24

First Level

Second Level

Third Level

Fourth Level

.,,,

.,, .

,,

Picturephone

Television

1

4

1

1

6

7

DS0DS1

DS2

DS3

DS4

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Digital Trunk

24DS0

T2Mux

(M1-2)

DS1

DS2

T3Mux

(M2-3)

DS3

DS1

DS1

DS1

DS2

DS2

DS2

DS2

DS2

DS2T4

Mux(M3-4)

DS3

DS3

DS3

DS3

DS3

DS4

T3Mux

(M1-3)28DS1

Level # Voice bps DS0 1 64k DS1 24 1.544M DS1c 48 3.152M DS2 96 6.312M DS3 672 44.736M DS4 4032 274.176M

North American Hierarchy

48DS0

T1Mux

(ChanBank)

1CMux

DS1C

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Waveform Coding TechniquesApplications

Digital hierarchy - T1 carrier - Bell system

Level Type Input Output

First Channel bank

24 *Voice

signals

T1(1.544 Mbps)

Second

Multiplexer 4 * T1Digital data

T2(6.312 Mbps)

Third Multiplexer 7 * T2 DPCM(Picturephone

)

T3(44.736 Mbps)

Fourth Multiplexer 6 * T3 PCM(Television)

T4(274.176

Mbps)

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T1 Carrier System Hierarchy of digital transmission formats that are used in

North America. The T stands for "Trunk". The basic unit of the T-carrier system is the DS-0, which is multiplexed to form transmission formats with higher speeds.

There exist four of them: T1, T2, T3 and T4. T1 is composed of 24 DS-0s. T2 = 4*T1. T3 = 7*T2. T4 = 6*T3.

Each of the T* units can also be referred to as a DS* unit, that is, T1=DS1, T2=DS2 etc.

The T-carrier system is quite similar to, and compatible with, the E-carrier system used in Europe, but it has lower capacity since it uses in-band signaling, or bit-robbing.

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T1 Carrier System The T1 carrier system was developed in the United

States in the early 1960s for digital voice communication over short-haul distances of 10-50 miles. Each channel (user) is first sampled at a rate of 8000 samples per second and quantised using 8 bit

companding. 24 voice channels are then combined into a composite

signal denoted as DS1. We thus have a total of 192 bits. One bit is added to this total for synchronisation purposes.

A 1010... sequence, in odd-numbered frames, is used for this purpose. There is a total of 193 bits in a frame of duration 1/8000 = 125ms.

The trunk rate is (193/125) x 106 = 1.544 Mbits/s.

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Waveform coding techniques Applications-Digital Multiplexers Basic problems involved in the design of

Digital Multiplexers- irrespective of its groupings

Synchronization : Demultiplexing requires that the bit rates of

signals are locked to a common clock; synchronization of the incoming signals is

necessary Framing : The multiplexed signal needs to

be encapsulated using framing to enable identification of individual components at the receiver

Handling of small variations / drift in input bit rates

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Bit stuffing : Used to cater for requirements of synchronization and rate adjustment to accommodate small variations in the input data rates

Outgoing bit rate of the mux is kept slightly higher than the sum of the maximum expected bit rates of the input channels

this is done by stuffing bits, which are additional non-information carrying bits

incoming signal is stuffed with no. of bits, as necessary, to raise its bit rate equal to that of a locally generated clock

at the demultiplexer, corresponding destuffing is carried out by removing the identified stuffed bits


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Bit Stuffing It was noted earlier that provision must be made to handle small

transmission-rate variations from users. To handle small rate variations, we can employ a bit stuffing technique.

Consider the arrangement as shown in Figure 18.9. Figure 18.9 Elastic buffer for bit stuffing. The data sequence from each user is fed into a elastic buffer at the

rate of R1 bits per second. The contents of this buffer are then fed to the input of the multiplexer at a higher rate, and the multiplexer also monitors the buffer contents.

If the input rate R1 begins to drop relative to the clock rate R'1, the buffer contents decrease. When the number of bits in the buffer drops below a predefined threshold level, the multiplexer disables readout ofthis buffer by the stuff signal, as shown in Figure 18.9. A bit is then stuffed. When the buffer contents rise above the threshold level, sampling of the buffer contents is resumed.

An example of the bit-stuffing process is shown in Figure 18.10. Bits are stuffed into the multiplexed data stream at time t = 3 when the input rate of user 1 drops below the threshold level and at time t = 6 when the input rate of user 2 drops below the threshold level.

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Designed to accommodate 24 voice channels primarily for short distance

human voice signal 300 Hz to 3400 Hz passed through a LPF with cut-off frequency

of 3.4 KHz before sampling W = 3.4 KHz, Nyquist rate = 6.8 KHz,

standard sampling rate in telephone systems is 8 KHz

each frame, therefore, occupies 125 µseconds

each frame comprises 24 * 8-bit words plus a synchronizing bit added at the end of the frame; total = 193 bits

T1 Carrier System

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T1 carrier (1.544 Mb/s)Digital part of phone system based on the T1 carrier:

193 bit frame (125 us, 8000 samples/s, 8 bits/sample/channel)

channel 1 channel 2 channel 3 channel 24

8 data bitsper channel

bit 1 is aframing code

Each channel has a data rateof 8000 samples/s * 8 bits/channel = 64 Kb/s

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Waveform coding techniques Applications-Digital Multiplexers Digital Multiplexers : T1 carrier system

frame size = 193 bits frame duration = 125 µseconds duration of each bit = 0.647 µseconds bit rate = 1.544 Mbps

Special Supervisory or signalling information needed to transmit information related to :

telephone off-hook dialled number telephone on-hook

in every sixth frame, the LSB of each voice channel is deleted

the signalling bit in inserted in the place of the LSB

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Super Frame For two reasons assignment of 8th digit in

every 6th frame to signaling and the need for two signaling paths for some switching systems it is necessary to identify a super frame of 12 frame in which the 6th and 12th frame contain two signaling paths. To achieve this and still allow for rapid synchronization of the receiver framing circuitry the frames are divided into odd and even frames.

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T1 System Framing Structure

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ApplicationsDigital Multiplexers : Bell system M12 MultiplexerSignal format

each frame is sub-divided into four sub-framesthese four sub-frames I, II, III, IV are transmitted in that order

IIIIIIIV

IIIIIIIV

SIGNAL FORMAT of BELL System M12 Multiplexer

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Three types of control Bits Needed to provide synchronization, frame indication, and to

identify which of the 4 input signals has been stuffed. These control bits are labeled as F, M and C F- Control Bit: two per sub frame. Constitute the main framing

pulse. The main framing sequence if F0F1F0F1F0F1F0F1 0r 01 01 01 01

M-Control Bits- 1 per sub frame forms secondary framing pulse. It is 0111

C-Control Bits- Three per sub frame are stuffing indicators. CI refers to input channel I CII refers to input channel II CIII refers to input channel III CIV refers to input channel IV

“000” for three Cs indicates no stuffing and “111” for three Cs indicates stuffing.

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Digital Hierarchy

The output of the M12 multiplexer is operating 136 kbs faster than the agragate rate of four DS1 6.312 vs 4x1.544=6.176

M12 frame has 1176 bits, i.e. 294-bit subframes ; each subframe is made of up of 49-bits blocks; each block starts with a control bit followed by a 4x12 info bits from four DS1 channels

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Makeup of a DS2 Frame

M1 01 02 03 04 C1 01 02 03 04 F0 01 02 03 04 C2 01 02 03 04 C3 01 02 03 04 F1 01 02 03 04

M1 01 02 03 04 C1 01 02 03 04 F0 01 02 03 04 C2 01 02 03 04 C3 01 02 03 04 F1 01 02 03 04

Bit stuffing

4 M bits (O11X X=0 alarm) C=000,111 bit stuffing

absent/present nominal stuffing rate 1796 bps,

max 5367

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M12 Multiplexer 12 bits from each (of the four) T1

inputs are interleaved to accumulate a total of 48 bits

control bits are inserted by the multiplexer

1 bit is inserted in between sequences of 48 data bits

each frame contains 24 control bits control bits are of 3 types : F, M , C

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M12 MultiplexerType

No. of bits per sub-frame

Description

F 2 main framing pulses

M 1 secondary framing pulses to identify the four sub-frames

C 3 stuffing indicatorsCI refers to input channel I, CII refers to II, …..

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M12 Multiplexer all three C-control bits set to 1

indicates that a stuffed bit has been inserted into that T1 signal; 0 → no stuffing

stuffed bit is inserted in the position of the first information bit of the T1 signal that follows the F1 control bit in the same sub-frame

a single error in any of the 3 C-control bits can be detected at the receiver by using majority logic

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M12 Multiplexer Demultiplexing : search for main framing sequence

F0F1F0F1F0F1F0F1 establishes identity for the four input T1 signals, M- and C-control bits

correct framing of the C-control bits is verified from the M0M1M1M1 sequence

finally the four T1 signals are properly demultiplexed and de-stuffed

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Waveform coding techniques Applications-Light Wave Transmission

Optical Fibre Cable links Advantages : low transmission

loss, high bandwidths, small size, light weight, immunity to EMI

Applications :long-haul, high-speed communications

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Optical Fibre Cable links Transmitter (Driver + Light Source) optical fiber waveguide Receiver

Transmitter input is binary data fed from the output

of a device like the digital multiplexer the driver for the light source is a low-

voltage-high-current device the driver turns the light source on or off

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light source consists of a laser injection device or a

semiconductor LED the on-off light pulses transmitted are

launched into the OFC Optical fiber waveguide:

source-to-fiber coupling loss fiber-loss or attenuation dispersion

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Receiver : regeneration of original data detection : light pulses are converted back

to electrical current pulses ; uses a photodiode to convert from power to current

pulse shaping and timing : amplification / filtering / equalization of electrical pulses and extraction of timing information

decision making : to decide that the received pulse is on or off

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Optical Link Loss Budget Analysis

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Vocoder





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Speech Quality of Various Coders

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How does DPCM calculate the difference between the current sample signal and a previous sample?

The first part of DPCM works exactly like PCM (that is why it is called differential PCM). The input signal is sampled at a constant sampling frequency (twice the input frequency). Then these samples are modulated using the PAM process. At this point, the DPCM process takes over.

The sampled input signal is stored in what is called a predictor. The predictor takes the stored sample signal and sends it through a differentiator. The differentiator compares the previous sample signal with the current sample signal and sends this difference to the quantizing and coding phase of PCM (this phase can be uniform quantizing or companding with A−law or u−law).

After quantizing and coding, the difference signal is transmitted to its final destination. At the receiving end of the network, everything is reversed. First the difference signal is dequantized. Then this difference signal is added to a sample signal stored in a predictor and sent to a low−pass filter that reconstructs the original input signal.

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Linear Predictive Coding (LPC) In DPCM, the value of the current

sample is guessed based on the previous sample. Can a better prediction be made ?

The answer is yes. For example, we can use the previous two samples to predict the current one

LPC is more general than DPCM. It exploit the correlation between multiple consecutive samples

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waveform coding techniques

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signal waveform

message signal

signal encoding

quantized signal

coded signal

analogue signal

analog signal modem

class of signal coders