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7/28/2019 3 Digitization

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Sampling First step in digitizing speech

Establish a set of discrete times at which the input waveform is

sampled Sampling Intervals

Regular

Irregular

Minimum sampling frequency is given by Nyquist theorem.

To reconstruct the original waveform from the sampled sequencethe sampling frequency must be at least twice the maximumfrequency of the original waveform.

Fs 2H

Fs=Sampling frequency or Nyquist rate

H=maximum frequency component in the analog waveform


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Sampling H is the bandwidth of the input waveform

In this case the waveform is reconstructed by passing the sampled

values through a low pass filter which smoothens out or interpolates

the signal between sampled values

vi(t) vo(t)

T TT

time time

1

0

vi(t)

Input Signal

WaveformSampled Signal

Waveform

(i)(ii) Sampling (iii)

...011101010011010011...

Samples are coded for transmission

(iv)

Analogue-to-digitalConverter

Digital-to-analogue

Converter

Sampled signal is recovered

(v)

Vi(t)


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PAM System

Sampling is a process of

multiplying a constant

amplitude impulse train

with the input signal

Like an Amplitude

modulation system where

pulse train acts as the

carrier

Called Pulse Amplitude

Modulation (PAM)


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Foldover Distortion

For a sine carrier

Frequency range is Fc-H to Fc+H (Fc is carrier frequency)

For PAM, the output spectrum contains the fundamental as well as

the harmonics of the fundamentals.

If the pulse train is square wave with 50% duty cycle, only the

fundamental and odd harmonics are present. The low pass filter at

the receiver end allows only the baseband component 0-H to pass.

If Fs is less than twice H, portions of PAM spectrum overlaps

This overlapping of the sidebands produces beat frequencies that

interfere with the desired signal and such an interference is referred

as aliasing or foldover distortion. The filter used for band limiting the

input speech waveform is known as antialiasing filter..


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Foldover Distortion

In digital speech system speech is sampled as 8KHz.

8KHz sampling results in oversampling.

This oversampling provides for the nonideal filter

characteristics such as lack of sharp cutoff.

The sampled signal is sufficiently attenuated at the

overlap frequency of 4 KHz. To adequately reduce the

energy level of the foldover spectrum


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Quantization and Binary Coding

Pulse amplitude modulation systems are not useful over long

distance, for the vulnerability of individual pulse amplitudes to noise,distortion and crosstalk.

The susceptibility of amplitude may be eliminated by converting the

PAM samples into a digital format. (Using regenerative repeaters) A finite number of bits are used for coding PAM samples.

n bit number can represent 2n samples.

PAM samples amplitude can take on an infinite range of values.

The PAM sample amplitude is quantized to the nearest of a range of

discrete amplitude levels.


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Quantization Process Signal V is confined to a range of VL

and VH. This range is divided into M(M=8) equal steps.

The step size S is given by

The center of each steps locate thequantization levels V0, V1V8.

Quantized signal Vq takes any of thequantized level value

A signal V is quantized to its nearestquantization level.

( )H LV VS =

The convention followed to quantize the signal is

Thus, the signal Vq makes quantum jump of step size S and at any instant of time thequantization error (V-Vq) has magnitude which is equal or less than S/2

The quantization in which the step size is uniform is called linear or uniform quantization.

q

q

V =V3 (if (V3-S/2) V< (V3+S/2)

V =V4 (if (V4-S/2) V< (V4+S/2)


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Quantization

Quantization brings about a certain amount of noise in immunity to the

signal.

Repeaters with quantizers are used after certain distance to control the

variation in instantaneous amplitude for attenuation and channel noise

within S/2.

If instantaneous noise level is larger than S/2, error occurs in the

quantization level.

The quantized signal is an approximate of the original signal. Quality can be increased by increasing the number of quantization levels

Sometimes increased levels introduces noise in the repeaters.

The susceptibility to noise can be greatly minimized by resorting the digital

coding of the PAM sample amplitude Each quantized level is represented by a code number and transmitted

instead of the level value.

If binary arithmetic is used the number will be transmitted as a series of

pulses.

Such a system is called PCM System.


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Binary PCM The analog signal is limited in

its excursions to the range -4

V to + 4V. The step size is 1 volt.

Eight quantization levels are

used and are located at -

3.5V, -2.5V ., +3.5V. Code

number 000 is assigned to -3.5V and so on.

If the analog samples are

transmitted the 1.3, 2.7, 0.5

etc will be transmitted.

If the quantized values are

transmitted voltages 1.5, 2.5,

0.5 etc will be transmitted

In binary PCM the binary

code patterns 101, 110,100are transmitted.


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PCM System The functional diagram for PCM is shown in the next figure

The analog input V is bandlimited to 3.4 KHz to prevent aliasing and

sampled at 8 KHZ.

Samples are quantized to produce PAM signals, and applied to encoder.

Encoder generates a unique pulse pattern for each quantized sample level.

The quantizer and encoder together work as Analog to Digital Converter

(ADC)

Receiver first separates the noise from the signals.

A qunatizer does it by determining the two voltage levels of the pulse.

Then it regenerates the appropriate pulse depending on the decision.

The regenerated pulse train is now fed to a decoder which assembles the

pulse pattern and generates a corresponding quantised voltage level. Qunatizer and decoder work together as a Digital to Analog converter

(DAC)

The quantized PAM is now passed through a filter which rejects the

frequency components lying outside the baseband signal.


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PCM System


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Digital Data, Digital Signal

Digital signal

Discrete, discontinuous voltage pulses

Each pulse is a signal element

Binary data encoded into signal elements


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Terms

Unipolar

All signal elements have same sign

Polar

One logic state represented by positivevoltage the other by negative voltage

Data rate

Rate of data transmission in bits per second

Duration or length of a bit

Time taken for transmitter to emit the bit


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Terms

Modulation rate

Rate at which the signal level changes

Measured in baud = signal elements per

second

Mark and Space

Binary 1 and Binary 0 respectively


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Interpreting Signals

Need to know

Timing of bits - when they start and end

Signal levels

Factors affecting successful interpreting ofsignals

Signal to noise ratio

Data rate Bandwidth


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Analogue to Digital

After sampling, the analogue amplitude value of each

sampled (PAM) signal is quantized into one of a numberof L discrete levels. The result is a quantized PAM

signal.

A codeword can then be used to designate each level at

each sample time. This procedure is referred to as Pulse Code Modulation .

Low-pass

Filter

Encoder;

Pulse

modulate

Sampler Quantizer

Continuous-

time

message

signal

PCM

wave

Quantized

PAM signal


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Encoding

After quantization, a digit is assigned to each of the

quantized signal levels in such a way that each level hasa one-to-one correspondence with the set of real

integers. This is called digitization of the waveform .

Each integer is then expressed as an n-bit binary

number, called codeword, or PCM word.

The number of codewords, M , is related to n by: 2n = M

Quantized

PAM

signal

A real

integer

PCM

codeword

(bit stream)

digitization To binary


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Codeword

Quantization followed by digitization maps input

amplitudes into PCM words.

A cell is the set of input amplitudes mapped to a

codeword.There are M integers, PCM words, or codewords

to correspond to the M allowed output

amplitudes of the quantizer.

Codebook is the set of all these M codewords.


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Analogue to Digital

time

Analoguewaveform

voltage

00000011010101111001101111011111

0010

010001101000101011001110

01

1110 1000 0100 0010 0000 0011 0101 1011

Bit stream

Sign bit

1 1 1 0 1 0 0 0 0 1 0 0 0 0 101 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1

PCM Codeword

3. Digitize into real integers

1. Sample analogue waveform at discrete times

2.

Quantize

intodiscre

televels

01234567

-1

-2-3-4-5-6-7

-7 -4 -2 -1 0 1 2 5

4. To binary


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Encoder Attributes

RZ (return to zero), NRZ (non-return to

zero)

Unipolar, Polar, Bipolar

Biphase


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NRZ coding may be unipolar or polar

1 0 1 1 0 11 0 01

UnipolarNRZ-L

Polar

NRZ-L


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NRZ-L Coding

NRZ-L (level):

1 higher level; 0 lower level

Used in SONET XOR bit sequence, and inearly magnetic tape recording

Long sequence of same bit causes

difficulty in clock recovery; also indetecting the average DC level


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NRZ pros and cons

Pros

Easy to engineer

Make good use of bandwidth

Cons dc component

Lack of synchronization capability

Used for magnetic recordingNot often used for signal transmission


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RZ Coding may be unipolar or bipolar

1 0 1 1 0 11 0 01

Unipolar

RZ

Bipolar

RZ


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RZ Coding may be unipolar or bipolar

Unipolar-RZ:

1 is represented by positive for the first half of T and zero for the

second half.

0 is represented by 0

Bipolar-RZ:

1 is represented by positive for the first half of T and zero for the

second half.

0 is represented by negative for the first half of T and zero for the

second half.

Used in baseband data transmission, magnetic

recording.

The transitions at T/2 may be used for synchronization.


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Quantization Noise

The quantized signal is an

approximation to the original signal andsome error.

The instantaneous errore= V-Vq is

randomly distributed within the range

S/2 and is called quantization error or

noise.

The mean square quantization error is

S2.

For linear quantization the probability

distribution of the error is constant

within the (S/2).


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Quantization Noise

The average qunatizationnoise output power is given by

the variance

Where =mean, which is zerofor qunatization noise.

The range of qunatization error

(S/2) determines the limits ofintegration.

/ 2

2 2

/ 2

/ 2

2

/ 2

/ 23

/ 2

2

1( 0)

1

1

3

12

S

S

S

S

S

S

e deS

e

S

e

S

S

=

=

=

=

2 2( ) ( )e p e de

=


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Quantization Noise

Signal to quantization noise ratio (SQR) is a good measure of

performance of a PCM system transmitting speech.

If Vr is the r.m.s. value of the input signal and the resistance level is

1 ohm, then SQR is given by

( ) ( )2

210log

12

10log(12) 20log

10.8 20log

r

r

r

VSQR dBS

VdBS

VdB

S

=

= +

= +


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Quantization Noise

If the input signal is a sinusoidal wave and Vm as the maximum

amplitude, SQR may be calculated from the full range sine wave as

( )

( )

2

210log122

10log(6) 20log

7.78 20log

m

m

m

V SSQR dB

V S dB

V S dB

=

= +

= +


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Quantization Noise

Expressing S in terms of Vm and the

number of steps, M, we have

( )( )

2

2 2

2

210log

4 12

10log(1.5 )20log(1.225 )

m

m

VSQR dB

V M

M dBM dB

=

==


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Quantization Noise

Quantity 1.225M represents the signal to quantization

noise voltage ratio for a full range sinusoidal input

voltage.

M=2n, where n is the number of bits used to code a

quantization level. Therefore

20log(1.225) 20 log(2)

1.76 6.02

SQR n dB

n dB

= +

= +


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Quantization Noise

The table is showing

the values of SQR fordifferent binary code

word sizes for

sinusoidal input

systems

Every additional code

bits gives an

increment of 6 dB in

SQR