413 feasibility

8/3/2019 413 Feasibility

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DOKUZ EYLUL UNIVERSITY

Faculty of Engineering

Electrical & Electronics Engineering Department

EE 413

DIGITAL COMMUNICATION SYSTEMS

PROJECT # 1

FEASIBILITY REPORT

2006502011 Onur NE2006502012 Samet DEVEL

18 November 2011


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THEORY

HOW IS SOUND RECORDED DIGITALLY?

Recording onto a tape is an example of analog recording. Audacity deals with digital

recordings - recordings that have been sampled so that they can be used by a digital computer,

like the one you're using now. Digital recording has a lot of benefits over analog recording.

Digital files can be copied as many times as you want, with no loss in quality, and they can be

burned to an audio CD or shared via the Internet. Digital audio files can also be edited much

more easily than analog tapes.

The main device used in digital recording is an Analog-to-Digital Converter (ADC).

The ADC captures a snapshot of the electric voltage on an audio line and represents it as a

digital number that can be sent to a computer. By capturing the voltage thousands of times per

second, you can get a very good approximation to the original audio signal:

Figure 1: Audio signal with audio samples

Each dot in the figure above represents one audio sample. There are two factors that

determine the quality of a digital recording:

Sample rate: The rate at which the samples are captured or played back, measured in

Hertz (Hz), or samples per second. An audio CD has a sample rate of 44,100 Hz, often

written as 44 KHz for short. This is also the default sample rate that Audacity uses,

because audio CDs are so prevalent.

Sample format orsample size: Essentially this is the number of digits in the digital

representation of each sample. Think of the sample rate as the horizontal precision of

the digital waveform, and the sample format as the vertical precision. An audio CD

has a precision of 16 bits, which corresponds to about 5 decimal digits.

Higher sampling rates allow a digital recording to accurately record higher frequencies

of sound. The sampling rate should be at least twice the highest frequency you want torepresent. Humans can't hear frequencies above about 20,000 Hz, so 44,100 Hz was chosen as


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the rate for audio CDs to just include all human frequencies. Sample rates of 96 and 192 KHz

are starting to become more common, particularly in DVD-Audio, but many people honestly

can't hear the difference.

Playback of digital audio uses a Digital-to-Analog Converter (DAC). This takes the

sample and sets a certain voltage on the analog outputs to recreate the signal, which the

Analog-to-Digital Converter originally took to create the sample. The DAC does this as

faithfully as possible and the first CD players did only that, which didn't sound good at all.

Nowadays DACs use Oversampling to smooth out the audio signal. The quality of the filters

in the DAC also contributes to the quality of the recreated analog audio signal. The filter is

part of a multitude of stages that make up a DAC.

PULSE - CODE MODULATION (PCM)

PCM is a digital transmission system with an analog-to-digital converter (ADC) at the

input and a digital-to-analog converter (DAC) at the output.

When the digital error probability is sufficiently small, PCM performance as an analog

communication system depends primarily on the quantization noise introduced by the ADC.

PCM Generation and Reconstruction

Figure 2: PCM Generation System

Figure 5 is the functional blocks of a PCM generation system. The analog input

waveform x(t) is lowpass filtered and sampled to obtain x(kTs). A quantizer rounds off the

sample values to the nearest discrete value in a set of q quantum levels. The resulting

quantized samples xq(kTs) are discrete in time (by virtue of sampling) and discrete in

amplitude (by virtue of quantizing).

To display the relationship between x(kTs) and xq(kTs), let the analog message be a

voltage waveform normalized such that . Uniform quantization subdivides the 2-

V peak to peak range into q equal steps of height 2/q V, as shown in figure 6.


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Figure 3: Quantization characteristic

The quantum levels are then taken to be at 1/q, 3/q, , (q-1)/q in the usual case

when q is an even integer. A quantized values such as corresponds to any

sample value in the range .

Next an encoder translates the quantized samples into digital code words. The encoder

works with M-ary digits and produces for each sample a codewords with digits per word,

unique encoding of the q different quantum levels requires that . The parameters

and should be chosen to satisfy the equality, so that

Thus, the number of quantum levels for binary PCM equals some power of 2, namely

.

Finally, successive codewords are read out serially to constitute the PCM waveform,

an M-ary digital signal. The PCM generator thereby acts as an ADC, performing analog - to

digital conversions at the sampling rate . A timing circuit coordinates the samplingand parallel - to serial read out.

Each encoded sampl is represented by a -digit output word, so the signaling rate

becomes with . Therefore, the bandwidth needed for PCM baseband

transmission is


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Fine grain quantization for accurate reconstruction of the message waveform

requires , which increases the transmission bandwidth by the factor times

the message bandwidth W.

Now consider a PCM receiver with the reconstruction system in figure 7.

Figure 4: PCM receiver

The received signal may be contaminated by noise, but regeneration yields a clean and nearly

errorless waveform if is sufficiently large. The DAC operations of serial to

parallel conversion, M-ary decoding, and sample and hold generate the analog waveform

drawn in figure 8. This waveform is a staircase approximation of , similar to flat

top sampling except that the sample values have been quantized. Lowpass filtering then

produces the smoothed output signal , which differs from the message to the extent

that the quantized samples differ from the exact sample values .

Figure 5: Reconstructed waveform

Perfect message reconstructed is therefore impossible in PCM, even when random

noise has no effect. The ADC operation at the transmitter introduces permanent errors that

appear at the receiver as quantization noise in the reconstructed signal.


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PROPOSAL

Learning objectives

In order to accomplish this project we have to know digital communicationtechniques. The learning subjects can be listed as below:

General Digital Communication Systems

o Source of the Digital Communication Systems

o Advantages & Disadvantages of Digital over Analog Systems

o The Main Blocks that forms the Digital Communication Systems

Learning MATLAB

o General functions that are going to be used

o Learning performance improvement algorithms

Source Encoding and Decoding

o Propose and Importance of the Coding

o Techniques for Source Coding & Decoding

o Detailed examination Pulse Code Modulation (PCM)

o Signal to Quantization Noise Ratio (SQNR)

Channels

o Types of the Channel Models

o Important Characteristics of the Channels

o Detailed Analysis of Additive White Gaussian Noise (AWGN)

Modulator & Demodulator

o The importance of these blocks

o Types of the Modulator & Demodulator

o Learning PSK technique

o Learning Gray Mapping Techniques

Channel Encoding & Decoding

o The Main Propose of this Coding

o Techniques for Channel Coding & Decoding

o Learning Convolution Code (Non-systematic) Techniques

o Viterbi Decoding Algorithm

o Important Characteristics and Issues that Affect the System Performance

o To evaluate the Bit Error Rate (BER)


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o Signal to Noise Ratios

o Preparation of some important performance test and their outputs

The Goal of This Project:

1. To understand the fundamentals of digital communications techniques.

2. To understand the underlying concepts of channel encoding decoding and baseband

digital modulation-demodulation.

3. To generate a white Gaussian noise sequence and to observe the effect of channel

noise with varying power on overall system performance.

4. To evaluate the Bit Error Rate (BER) versus signal to noise ratio (SNR) of a digital

communication system.

MATLAB CODES

Analog to Digital Conversion (ADC)

%EE413_Digital Communication Systems

%Project 1

%Group Members: ONUR NE - SAMET DEVEL

%ADC- Analog to Digital Conversion

clc

clear all

close all

Fs = 8000;%sampling frequency

n=3;%digits is eqal to n-1

x=sin(2*pi*(0:(Fs-1))/Fs); %sampling equation of sinusoidal input signal

%eps returns the distance from 1.0 to the next largest double-precision

%number

%find(x)= Find indices and values of nonzero elements

x(find(x>=1))=(1-eps);

%B = floor(A) rounds the elements of A to the nearest integers less than or

%equal to A.For complex A, the imaginary and real parts are rounded

%independently.

xq=floor((x+1)*2^(n-1)); %quantized samples signal

xq=xq/(2^(n-1));

xq=xq-(2^(n)-1)/2^(n);

stem(xq) %quantized signal plot

grid on


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hold on

plot(x,'r') %sinusoidal sampling signal plot

xlabel('fs')

ylabel('voltage')

title('quantized signal and sinusoidal sampling signal(red one)')

figure

plot(x,xq) %quantization characteristic screen

grid on

xlabel('x(kTs)')

ylabel('xq(kTs)')

title('quantizatation characteristic')

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0

- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

f s

v

o

lta

g

e

q u a n t i z e d s i g n a l a n d s i n u s o i d a l l i i


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- 1 - 0 . 8 - 0 . 6 - 0 . 4 - 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

x ( k T s )

x

q(kT

s

)

q u a n t i z a t a t i o n c h a r a c t e r i s t i c

Digital to Analog Conversion (DAC)

%EE413_Digital Communication Systems

%Project 1

%Group Members: ONUR NE - SAMET DEVEL

%DAC- Digital to Analog Conversion

clc

clear all

close all

Fs = 8000;%sampling frequency

n=6;%digits is equal to n-1

x=sin(2*pi*(0:(Fs-1))/Fs); %sinusoidal input signal

%eps returns the distance from 1.0 to the next largest double-precision

%number

%find(x)= Find indices and values of nonzero elements

x(find(x>=1))=(1-eps);

%B = floor(A) rounds the elements of A to the nearest integers less than or

%equal to A.For complex A, the imaginary and real parts are rounded

%independently.

xq=floor((x+1)*2^(n-1)); %quantized samples signal

xq=xq/(2^(n-1));

xq=xq-(2^(n)-1)/2^(n);

stem(xq) %quantized signal plot


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grid on

hold on


xlabel('fs')

ylabel('voltage')

title('quantized signal and sinusoidal sampling signal(red one)')

figure

plot(x,xq) %quantization characteristic screen

grid on

xlabel('x(kTs)')

ylabel('xq(kTs)')

title('quantizatation characteristic')

k=0:7999; %sample

m = 0:length(xq)-1;

for i=1:length(k)y(i) = sum(xq.*sinc(m- k(i)));

end

figure

plot(k,y); %DAC signal

hold on


title('DAC signal and sinusoidal signal plot(red one)')

grid on

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0- 1

- 0 . 8

- 0 . 6

- 0 . 4

- 0 . 2

0

0 . 2

0 . 4

0 . 6

0 . 8

1

f s

voltage

q u a n t iz e d s i g n a l a n d s in u s o i d a l s a m p l i n g s i g n a l ( r


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-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

x(kTs)

xq(kTs)

quantizatation characteristic

0 1000 2000 3000 4000 5000 6000 7000 8000-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1DAC signal and sinusoidal signal plot(red one)


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GROUP WORK PLAN

After taking project and researching some information about project topic, we

determine tasks about project studying time. For this aim, we prepare gantt chart. This table

includes planning programs for time duration. Both group members are responsible for each

tasks.

Task \ Date Nov/15Nov/1

8Nov/2

2Nov/2

9Dec/6

Preparing a feasibility report

A/D and D/A conversion using MATLAB

Preparing Interim Report 1

Modulator-demodulator using MATLAB

Preparing Interim Report 2

Channel encoder/decoder using MATLAB

Designing a GUI

Preparing poster presentation

Writing final report

REFERENCES

Communication Systems, A. Bruce Carlson, Paul B. Crilly, Janet C.Rutledge, Mc

Graw Hill

Modern Digital and Analog Communication Systems, B. P. Lathi, Oxford

University Press 1998

Communication Systems, Simon Haykin, John Wiley & Sons, Inc.

413 feasibility

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