DC Lecture5

8/12/2019 DC Lecture5

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Lecture # 5:


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Practical Sampling Rates Speech

- Telephone quality speech has a bandwidth of 4 kHz(actually 300 to 3300Hz)

- Most digital telephone systems are sampled at 8000samples/sec

Audio:- The highest frequency the human ear can hear is

approximately 15kHz

- CD quality audio are sampled at rate of 44,000

samples/sec Video

- The human eye requires samples at a rate of at least 20frames/sec to achieve smooth motion


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Pulse Code Modulation PCM)

Pulse Code Modulation refers to a digital baseband signal that isgenerated directly from the quantizer output

Sometimes the term PCM is used interchangeably with quantization

Other methods

PWM (Pulse Width Modulation) PPM (Pulse Position Modulation)


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Advantages of PCM:

Relatively inexpensive

Easily multiplexed: PCM waveforms from different

sources can be transmitted over a common digital

channel (TDM)

Easily regenerated: useful for long-distance

communication, e.g. telephone

Better noise performance than analog system

Signals may be stored and time-scaled efficiently (e.g.,

satellite communication)

Efficient codes are readily available

Disadvantage:

Requires wider bandwidth than analog signals


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2.5 Sources of Corruption in the sampled,quantized and transmitted pulses Sampling and Quantizat ion Effects

Quantization (Granularity) Noise:Results whenquantization levels are not finely spaced apart enoughto accurately approximate input signal resulting intruncation or rounding error.

Quantizer Saturation or Overload Noise:Results wheninput signal is larger in magnitude than highestquantization level resulting in clipping of the signal.

Timing Jitter:Error caused by a shift in the sampler

position. Can be isolated with stable clock reference.

Channel Effects

Channel Noise

Intersymbol Interference (ISI)


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The level of quantization noise is dependent on how close anyparticular sample is to one of the L levels in the converter

For a speech input, this quantization error resembles a noise-like disturbance at the output of a DAC converter

Signal to Quantization Noise Ratio


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Uniform Quantization A quantizer with equal quantization level is a Uniform Quantizer

Each sample is approximated within a quantile interval Uniform quantizers are optimal when the input distribution is

uniform

i.e. when all values within the range are equally likely

Most ADCs are implemented using uniform quantizers

Error of a uniform quantizer is bounded by


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Quantization Levels


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The mean-squared value (noise variance) of the quantization error isgiven by:

2/

2/

2)(2/

2/

2/

2/

112)()(2)(2 q

q

deeq

q

q

q qdeqedeepe

12

22/

2/3

31 qq

q

eq

Signal to Quantization Noise Ratio


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The peak power of the analog signal can be expressed as:

Therefore the Signal to Quatization Noise Ratio is given by:

)4

22()

2

2(2 qLVV ppp

23LSNRq


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where L = 2nis the number of quantization levels for the converter.

(n is the number of bits).

Since L = 2n, SNR = 22nor in decibels

LppV

q

dBnn

dBN

S 6)22(

10

log10

If q is the step size, then the maximum quantization error that canoccur in the sampled output of an A/D converter is q


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Nonuniform Quantization Nonuni form quant izershave unequally spaced levels

The spacing can be chosen to optimize the Signal-to-Noise Ratiofor a particular type of signal

It is characterized by:

Variable step size

Quantizer size depend on signal size

Sometimes non-uniform spacing is preferred to uniform spacing

Many signals such as speech have a nonuniform distribution

More amplitude is close to zero than a high level (see Fig. 2.17)

Basic principleis to use more levels at regions with large

probability density function (pdf) Concentrate quantization levels in areas of largest pdf

Or use fine quantization (small step size) for weak signals and

coarse quantization (large step size) for strong signals


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Companding Companding is a method of reducing the number of bits required in

ADC while achieving an equivalent dynamic range or SQNR

In order to improve the resolution of weak signals within a converter,

and hence enhance the SQNR, the weak signals need to be

enlarged, or the qu ant izat ion s tep size decreased, but only for the

weak signals

But strong signals can potentially be reduced without significantly

degrading the SQNR or alternatively increasing quantization step size The compression process at the transmitter must be matched with an

equivalent expansion process at the receiver


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Input/Output Relationship of Compander

Logarithmic expression Y = log X is the most commonly usedcompander

Taking the log of Y = log X reduces the dynamic range sinceloge(1+x) x if x 0

This is effective in speech and music which often have smallabsolute values


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Types of Companding-Law Companding Standard (North & South

America, and Japan)

where

x and y represent the input and output voltages

is a constant number determined by experiment

In the U.S., telephone lines uses companding with = 255

Samples 4 kHz speech waveform at 8,000 sample/sec

Encodes each sample with 8 bits, L = 256 quantizer levels

Hence data rate R = 64 kbit/sec

= 0 corresponds to uniform quantization


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A-Law Companding Standard (Europe, China, Russia,

Asia, Africa)

where

x and y represent the input and output voltages

A = 87.6

A is a constant number determined by experiment


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Pulse Modulation Recall that analog signals can be represented by a sequence of discrete

samples (output of sampler)

APM results when some characteristic of the pulse (amplitude, width orposition) is varied in correspondence with the data signal

Can be obtained either by Natural or Flat top Sampling

Two Types:

Pulse Amplitude Modulation (PAM)

The amplitude of the periodic pulse train is varied in proportion to thesample values of the analog signal

Pulse Time Modulation

Encodes the sample values into the time axis of the digital signal

Pulse Width Modulation (PWM)

Constant amplitude, width varied in proportion to the signal Pulse Duration Modulation (PDM)

sample values of the analog waveform are used in determining

the width of the pulse signal


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PCM Waveform Types The output of the A/D converter is a set of binary bits

But binary bits are just abstract entities that have no physical

definition We use pulses to convey a bit of information, e.g.,

In order to transmit the bits over a physical channel they must betransformed into a physical waveform

A l ine coder or baseband binary transm itter transforms a streamof bits into a physical waveform suitable for transmission over a

channel Line coders use the terminology mark for 1 and space to mean 0

In baseband systems, binary data can be transmitted using manykinds of pulses


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There are many types of waveforms. Why? performance criteria! Each line code type have merits and demerits

The choice of waveform depends on operating characteristics of a

system such as

Modulation-demodulation requirements

Bandwidth requirement

Synchronization requirement

Receiver complexity, etc.,


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Goals of Line Coding (qualities to look for)

A line code is designed to meet one or more of the following goals:

Self-synchronization

The ability to recover timing from the signal itself

That is, self-clocking (self-synchronization) - ease of clock lock

or signal recovery for symbol synchronization

Long series of ones and zeros could cause a problem

Low probability of bit error Receiver needs to be able to distinguish the waveform associated

with a mark from the waveform associated with a space

BER performance

relative immunity to noise

Error detection capability

enhances low probability of error


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Spectrum Suitable for the channel

Spectrum matching of the channel

e.g. presence or absence of DC level

In some cases DC components should be avoided

The transmission bandwidth should be minimized

Power Spectral Density

Particularly its value at zero

PSD of code should be negligible at the frequency near zero Transmission Bandwidth

Should be as small as possible

Transparency

The property that any arbitrary symbol or bit pattern can be

transmitted and received, i.e., all possible data sequence should

be faithfully reproducible


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Line Coder The input to the line encoder is

the output of the A/D converter

or a sequence of values an

that is a function of the data bit

The output of the line encoder

is a waveform:

where f(t) is the pulse shape and Tbis the bit period (Tb=Ts/nfor n bit quantizer)

This means that each line code is described by a symbol mappingfunction anand pulse shape f(t)

Details of this operation are set by the type of line code that is beingused


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Summary of Major Line Codes Categories of Line Codes

Polar - Send pulse or negative of pulse

Unipolar - Send pulse or a 0

Bipolar (a.k.a. alternate mark inversion, pseudoternary)

Represent 1 by alternating signed pulses

Generalized Pulse Shapes

NRZ -Pulse lasts entire bit period

Polar NRZ

Bipolar NRZ

RZ - Return to Zero - pulse lasts just half of bit period

Polar RZ

Bipolar RZ Manchester Line Code

Send a 2- pulse for either 1 (highlow) or 0 (lowhigh)

Includes rising and falling edge in each pulse


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No DC component

HS ( Half Sine)

When the category and the generalized shapes are combined, we

have the following:

Polar NRZ:

Wireless, radio, and satellite applications primarily use Polar

NRZ because bandwidth is precious

Unipolar NRZ

Turn the pulse ON for a 1, leave the pulse OFF for a 0

Useful for noncoherent communication where receiver cant

decide the sign of a pulse

fiber optic communication often use this signaling format

Unipolar RZ RZ signaling has both a rising and falling edge of the pulse

This can be useful for timing and synchronization purposes


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Bipolar RZ

A unipolar line code, except now we alternate betweenpositive and negative pulses to send a 1

Alternating like this eliminates the DC component This is desirable for many channels that cannot transmit the

DC components

Generalized Grouping

Non-Return-to-Zero: NRZ-L, NRZ-M NRZ-S

Return-to-Zero: Unipolar, Bipolar, AMI Phase-Coded: bi-f-L, bi-f-M, bi-f-S, Miller, Delay Modulation

Multilevel Binary: dicode, doubinary

Note:There are many other variations of line codes (see Fig. 2.22,page 80 for more)


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Commonly Used Line Codes Polar line codes use the antipodal mapping

Polar NRZ uses NRZ pulse shape

Polar RZ uses RZ pulse shape


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Unipolar NRZ Line Code

Unipolar non-return-to-zero (NRZ) line code is defined by

unipolar mapping

In addition, the pulse shape for unipolar NRZ is:

where Tbis the bit period


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Bipolar Line Codes

With bipo lar l ine codes a space is mapped to zero and

a mark is alternately mapped to -A and +A

It is also called pseudoternarysignaling or alternate mark inversion(AMI)

Either RZ or NRZ pulse shape can be used


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Manchester Line Codes

Manchester line codes use the antipodal mappingand the following spl i t -phase pulse shape:


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Summary of Line Codes


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Comparison of Line Codes Self-synchronization

Manchester codes have built in timing information because theyalways have a zero crossing in the center of the pulse

Polar RZ codes tend to be good because the signal level always

goes to zero for the second half of the pulse

NRZ signals are not good for self-synchronization

Error probability

Polar codes perform better (are more energy efficient) than

Unipolar or Bipolar codes

Channel characteristics

We need to find the power spectral density (PSD) of the linecodes to compare the line codes in terms of the channel

characteristics


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Generation of Line Codes

The FIR filter realizes the different pulse shapes

Baseband modulation with arbitrary pulse shapes can bedetected by

correlation detector

matched filter detector (this is the most common detector)

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