ec6501 digital communication objectives: to know the principles of sampling & quantization to...

EC6501 DIGITAL COMMUNICATION

OBJECTIVES:

To know the principles of sampling & quantization

To study the various waveform coding schemes To learn the various baseband transmission

schemes To understand the various Band pass signaling

schemes To know the fundamentals of channel coding

SYLLABUS UNIT I SAMPLING & QUANTIZATION 9

Low pass sampling – Aliasing- Signal Reconstruction-Quantization - Uniform & non-uniform quantization - quantization noise - Logarithmic Companding of speech signal- PCM - TDM 56

UNIT II WAVEFORM CODING 9

Prediction filtering and DPCM - Delta Modulation - ADPCM & ADM principles-Linear Predictive Coding

UNIT III BASEBAND TRANSMISSION 9

Properties of Line codes- Power Spectral Density of Unipolar / Polar RZ & NRZ – Bipolar NRZ - Manchester- ISI – Nyquist criterion for distortionless transmission – Pulse shaping – Correlative coding - Mary schemes – Eye pattern - Equalization

UNIT IV DIGITAL MODULATION SCHEME 9

Geometric Representation of signals - Generation, detection, PSD & BER of Coherent BPSK, BFSK & QPSK - QAM - Carrier Synchronization - structure of Non-coherent Receivers - Principle of DPSK.

UNIT V ERROR CONTROL CODING 9

Channel coding theorem - Linear Block codes - Hamming codes - Cyclic codes - Convolutional codes - Vitterbi Decoder

TOTAL: 45 PERIODS

OUTCOMESUpon completion of the course, students will be

able to Design PCM systems Design and implement base band transmission

schemes Design and implement band pass signaling

schemes Analyze the spectral characteristics of band pass

signaling schemes and their noise performance Design error control coding schemes

EC6501 DIGITAL COMMUNICATION

UNIT - 1

INTRODUCTION

UNIT I SAMPLING & QUANTIZATION (9)

Low pass sampling Aliasing Signal Reconstruction Quantization Uniform & non-uniform quantization Quantization Noise Logarithmic Companding of speech signal PCM TDM

12

Digital communication system

Low Pass Filter

Sampler Quantizer Channel Encoder

Line Encoder

Pulse Shaping

Filters

SourceEncoder

Modulator

MultiplexerInputSignalAnalog/Digital

To Channel

DetectorReceiverFilter

De-Modulator

From Channel

Channel Decoder

Digital-to-AnalogConverter

De-Multiplexer

Signalat the user end

Carrier

Carrier Ref.

Key Questions

How can a continuous wave form be converted into discrete samples?

How can discrete samples be converted back into a continuous form?

Low Pass Sampling

Sampling (in time) is

Measure amplitude at regular intervals

How many times should we sample?

Nyquist TheoremFor lossless digitization, the sampling rate should be at least twice the maximum frequency of the signal to be sampled.

In mathematical terms:fs > 2*fm

where fs is sampling frequency and fm is the maximum frequency in the signal

Limited Sampling

But what if one cannot sample fast enough?

Limited Sampling

Reduce signal frequency to half of maximum sampling frequency

low-pass filter removes higher-frequencies

(e.g.) If max sampling frequency is 22kHz, the it is a must to low-pass filter a signal down to 11kHz

Aliasing effect

LP filter

Nyquist rate

aliasing

Three different sampling methodsPractical Sampling Methods are Natural Sampling and Flat-top Sampling

Natural Sampling

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Pulse-Amplitude Modulation

• Pulse-Amplitude Modulation (PAM)– The amplitude of regularly spaced pulses are

varied in proportion to the corresponding sample values of a continuous message signal.

– Two operations involved in the generation of the PAM signal

• Instantaneous sampling of the message signal m(t) every Ts seconds,

• Lengthening the duration of each sample, so that it occupies some finite value T.

Fig. 5

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Fig.5Back Next

30

Fig.6 Back Next

31

Fig.7Back Next

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• The advantages offered by digital pulse modulation– Performance

• Digital pulse modulation permits the use of regenerative repeaters, when placed along the transmission path at short enough distances, can practically eliminate the degrading effects of channel noise and signal distortion.

– Ruggedness• A digital communication system can be designed to withstand the

effects of channel noise and signal distortion– Reliability

• Can be made highly reliable by exploiting powerful error-control coding techniques.

– Security• Can be made highly secure by exploiting powerful encryption

algorithms– Efficiency

• Inherently more efficient than analog communication system in the tradeoff between transmission bandwidth and signal-to-noise ratio

– System integration• To integrate digitized analog signals with digital computer data

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Quantization Process

• Amplitude quantization– The process of transforming the sample amplitude m(nTs) of a

baseband signal m(t) at time t=nTs into a discrete amplitude v(nTs) taken from a finite set of possible levels.

– Representation level (or Reconstruction level)• The amplitudes vk , k=1,2,3,……,L

– Quantum (or step-size)• The spacing between two adjacent representation levels

)17(,...,2,1},{: 1 LkmmmI kkk

)18()(mgv

Fig. 9

Fig. 10

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Fig.9Back Next

35

Fig.10 Back Next

Two types of quantization area) Mid-tread b) Mid-rise

Linear Quantization• Applicable when the signal is in a

finite range (fmin, fmax)• The entire data range is divided

into L equal intervals of length Q (known as quantization interval or quantization step-size)

• Q=(fmax-fmin)/L Interval i is mapped to the middle value of this interval

• We store/send only the index of quantized value min

Signal Range is Symmetric

Quantization Noise

Non-Uniform Quantization

Many signals such as speech have a nonuniform distribution.– The amplitude is more likely to be close to zero than to be at higher levels.

Nonuniform quantizers have unequally spaced levels– The spacing can be chosen to optimize the SNR for a particular type of signal.

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2 4 6 8

2

4

6

-2

-4

-6

Input sampleX

Output sampleXQ

-2-4-6-8

Example: Nonuniform 3 bit quantizer

Non-Linear Quantization

• The quantizing intervals are not of equal size• Small quantizing intervals are allocated to small

signal values (samples) and large quantization intervals to large samples so that the signal-to-quantization distortion ratio is nearly independent of the signal level

• S/N ratios for weak signals are much better but are slightly less for the stronger signals

• “Companding” is used to quantize signals

Function representation

Uniform and Non-uniform Quantization

Companding

• Formed from the words compressing and expanding.

• A PCM compression technique where analogue signal values are rounded on a non-linear scale.

• The data is compressed before sent and then expanded at the receiving end using the same non-linear scale.

• Companding reduces the noise and crosstalk levels at the receiver.

u-LAW and A-LAW definitions

• A-law and u-law are companding schemes used in telephone networks to get more dynamics to the 8 bit samples that is available with linear coding.

• Typically 12..14 bit samples (linear scale) sampled at 8 kHz sample are companded to 8 bit (logarithmic scale) for transmission over 64 kbit/s data channel.

• In the receiving end the data is then converted back to linear scale (12..14 bit) and played back. converted back

45

– Compressor • A particular form of compression law : μ-law

• μ-law is neither strictly linear nor strictly logarithmic

• A-law :

)25.5(

11

,log1

)log(1

10,

log1

m

AA

mA

Am

A

mA

v

)26.5(

11

,)log1(

10,

log1

m

AmA

Am

A

A

vd

md

)23.5()1log(

)1log(

mv

)24.5()1()1log(

mvd

md

Fig. 5.11

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Fig.11 Back Next

Example: m-law Companding

Eeng 360 47

2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

0

0.5

1

2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

0

0.5

1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

0

0.5

1

x[n]=speech /song/

y[n]=C(x[n])Companded Signal

Segment of x[n]

Segment of y[n]Companded Signal

Close View of the Signal

A-law and -m law Companding• These two are standard companding methods. • u-Law is used in North America and Japan• A-Law is used elsewhere to compress digital telephone signals

Eeng 360 48

Technical Presentation Page 49

Quantization - why do we need such classification ?! - (3)

Comparison – Uniform Vs. Non-Uniform Usage

Speech signals doesn’t require high quantization resolution for high amplitudes (50% Vs. 15%). wasteful to use uniform quantizer ? The goal is decrease the SQNR, more levels for low amplitudes, less levels for high ones. Maybe use a Non-uniform quantizer ?

Technical Presentation Page 50

Concepts

Quantization

More About Non-Uniform Quantizers (Companding)

Uniform quantizer = use more levels when you need it. The human ear follows a logarithmic process in which high amplitude sound doesn’t require the same resolution as low amplitude sounds. One way to achieve non-uniform quantization is to use what is called as “Companding” Companding = “Compression + Expanding”

Compressor Function

UniformQuantization

Expander Function

(-1)

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Pulse-Code Modulation• PCM (Pulse-Code Modulation)

– A message signal is represented by a sequence of coded pulses, which is accomplished by representing the signal in discrete form in both time and amplitude

– The basic operation• Transmitter : sampling, quantization, encoding• Receiver : regeneration, decoding, reconstruction

• Operation in the Transmitter1. Sampling

1. The incoming message signal is sampled with a train of rectangular pulses2. The reduction of the continuously varying message signal to a limited

number of discrete values per second2. Nonuniform Quantization

1. The step size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end-step of the quantizer can take care of possible excursions of the voice signal into the large amplitude ranges that occur relatively infrequently.

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Fig.11 Back Next

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3. Encoding1.To translate the discrete set of sample vales to a

more appropriate form of signal2.A binary code

The maximum advantage over the effects of noise in a transmission medium is obtained by using a binary code, because a binary symbol withstands a relatively high level of noise.

The binary code is easy to generate and regenerate

Table. 2

Fig. 11

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• Regeneration Along the Transmission Path– The ability to control the effects of distortion and noise produced by

transmitting a PCM signal over a channel– Equalizer

• Shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the transmission

– Timing circuitry• Provides a periodic pulse train, derived from the received pulses• Renewed sampling of the equalized pulses

– Decision-making device• The sample so extracted is compared o a predetermined threshold

– ideally, except for delay, the regenerated signal is exactly the same as the information-bearing signal

1. The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal

2. If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion.

Fig. 13

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Fig.13Back Next

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• Operations in the Receivers

1. Decoding and expanding1.Decoding : regenerating a pulse whose amplitude is

the linear sum of all the pulses in the code word2.Expander : a subsystem in the receiver with a

characteristic complementary to the compressor1. The combination of a compressor and an expander is a

compander

2. Reconstruction1.Recover the message signal : passing the expander

output through a low-pass reconstruction filter

Categories of multiplexing

Time Division Multiplexing (TDM)

TDM is a technique used for transmitting several message signals over a single communication channel by dividing the time frame into slots, one slot for each message signal

• Entire spectrum is allocated for a channel (user) for a limited time. • The user must not transmit until its next turn.• Used in 2nd generation

• Advantages:– Only one carrier in the medium at any given time– High throughput even for many users– Common TX component design, only one power amplifier– Flexible allocation of resources (multiple time slots).

f

t

c

k2 k3 k4 k5 k6k1

Frequency

Time

Time Division Multiplexing

Time Division Multiplexing

• Disadvantages– Synchronization – Requires terminal to support a much higher data

rate than the user information rate therefore possible problems with intersymbol-interference.

• Application: GSM GSM handsets transmit data at a rate of 270 kbit/s in

a 200 kHz channel using GMSK modulation. Each frequency channel is assigned 8 users, each

having a basic data rate of around 13 kbit/s

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Time Division MultiplexingAt the Transmitter

Simultaneous transmission of several signals on a time-sharing basis.

Each signal occupies its own distinct time slot, using all frequencies, for the duration of the transmission.

Slots may be permanently assigned on demand.

At the Receiver

Decommutator (sampler) has to be synchronized with the incoming waveform Frame Synchronization

Low pass filter

ISI – poor channel filtering

Feedthrough of one channel's signal into another channel -- Crosstalk

Applications of TDM: Digital Telephony, Data communications, Satellite Access, Cellular radio.

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Time Division Multiplexing

Conceptual diagram of multiplexing-demultiplexing.

PAM TDM System

TDM-PAM: Transmitter

TDM-PAM : Receiver

Samples of Signal -1

time

0 Ts 2Ts

g1(t)

Samples of signal - 2

Ts Ts

g2(t)

Multiplexing of TWO signals

0 Ts 2Ts

TDM-PAM for 4 signals.

1 1 12 2 2

3 3 3

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4

Time

Problem

Two low-pass signals of equal bandwidth are sampled and time division multiplexed using PAM. The TDM signal is passed through a Low-pass filter & then transmitted over a channel with a bandwidth of 10KHz.

Continued….

Problem (continued…)

a) What is maximum Sampling rate for each Channel?

b) What is the maximum frequency content allowable for each signal?

Problem: Solution

Channel Bandwidth = 10 KHz.Number of samples that can be transmitted

through the channel = 20KMaximum Sampling rate for each channel =

10K Samples/sec.Maximum Frequency for each Signal = 5KHz

End of Unit-1