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