digital communication- introduction
DESCRIPTION
introduction of digital communicationTRANSCRIPT
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Digital Communication
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Communication System
Source of Information
Destination Information
Transmitter ReceiverChannel
Communication System
Transmitted Signal
Received Signal
Voice, Video, data
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Data Communication Terms Data - entities that convey meaning, or
information Signals - electric or electromagnetic
representations of data Transmission - communication of data by
the propagation and processing of signals
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Examples of Analog and Digital Data Analog
Video Audio
Digital Text Integers
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Analog Signal
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Digital Signal
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Analog Signals A continuously varying electromagnetic wave that
may be propagated over a variety of media, depending on frequency
Examples of media: Copper wire media (twisted pair and coaxial cable) Fiber optic cable Atmosphere or space propagation
Analog signals can propagate analog and digital data
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Digital Signals A sequence of voltage pulses that may be
transmitted over a copper wire medium Generally cheaper than analog signaling Less susceptible to noise interference Suffer more from attenuation Digital signals can propagate analog and
digital data
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Analog Signaling
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Digital Signaling
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Time-Domain Concepts Analog signal - signal intensity varies in a smooth
fashion over time No breaks or discontinuities in the signal
Digital signal - signal intensity maintains a constant level for some period of time and then changes to another constant level
Periodic signal - analog or digital signal pattern that repeats over time s(t +T ) = s(t ) where T is the period of the signal
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Time-Domain Concepts Aperiodic signal - analog or digital signal pattern
that doesn't repeat over time Peak amplitude (A) - maximum value or strength
of the signal over time; typically measured in volts Frequency (f )
Rate, in cycles per second, or Hertz (Hz) at which the signal repeats
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Time-Domain Concepts Period (T ) - amount of time it takes for one
repetition of the signal T = 1/f
Phase () - measure of the relative position in time within a single period of a signal
Wavelength () - distance occupied by a single cycle of the signal Or, the distance between two points of corresponding
phase of two consecutive cycles
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Sine Wave Parameters General sine wave
s(t ) = A sin(2ft + ) Figure shows the effect of varying each of the
three parameters (a) A = 1, f = 1 Hz, = 0; thus T = 1s (b) Reduced peak amplitude; A=0.5 (c) Increased frequency; f = 2, thus T = ½ (d) Phase shift; = /4 radians (45 degrees)
note: 2 radians = 360° = 1 period
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Sine Wave Parameters
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Frequency-Domain Concepts Fundamental frequency - when all frequency
components of a signal are integer multiples of one frequency, it’s referred to as the fundamental frequency
Spectrum - range of frequencies that a signal contains
Absolute bandwidth - width of the spectrum of a signal
Effective bandwidth (or just bandwidth) - narrow band of frequencies that most of the signal’s energy is contained in
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Frequency-Domain Concepts Any electromagnetic signal can be shown to
consist of a collection of periodic analog signals (sine waves) at different amplitudes, frequencies, and phases
The period of the total signal is equal to the period of the fundamental frequency
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Relationship between Data Rate and Bandwidth
The greater the bandwidth, the higher the information-carrying capacity
Conclusions Any digital waveform will have infinite bandwidth BUT the transmission system will limit the bandwidth
that can be transmitted AND, for any given medium, the greater the bandwidth
transmitted, the greater the cost HOWEVER, limiting the bandwidth creates distortions
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Reasons for Choosing Data and Signal Combinations Digital data, digital signal
Equipment for encoding is less expensive than digital-to-analog equipment
Analog data, digital signal Conversion permits use of modern digital transmission
and switching equipment Digital data, analog signal
Some transmission media will only propagate analog signals
Examples include optical fiber and satellite Analog data, analog signal
Analog data easily converted to analog signal
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Analog Transmission Transmit analog signals without regard to
content Attenuation limits length of transmission
link Cascaded amplifiers boost signal’s energy
for longer distances but cause distortion Analog data can tolerate distortion Introduces errors in digital data
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Digital Transmission Concerned with the content of the signal Attenuation endangers integrity of data Digital Signal
Repeaters achieve greater distance Repeaters recover the signal and retransmit
Analog signal carrying digital data Retransmission device recovers the digital data from
analog signal Generates new, clean analog signal
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About Channel Capacity Impairments such as noise, limit the data
rates that can be achieved. For digital data, to what extent do
impairments limit data rate? Channel Capacity – the maximum rate at
which data can be transmitted over a given communication path, or channel, under given conditions
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Concepts Related to Channel Capacity
Data rate - rate at which data can be communicated (bps)
Bandwidth - the bandwidth of the transmitted signal as constrained by the transmitter and the nature of the transmission medium (Hertz)
Noise - average level of noise over the communications path
Error rate - Rate at which errors occur Error = transmit 1 and receive 0; transmit 0 and receive
1
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Nyquist Bandwidth For binary signals (two voltage levels)
C = 2B With multilevel signaling
C = 2B log2 M M = number of discrete signal or voltage levels
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Signal-to-Noise Ratio Ratio of the power in a signal to the power
contained in the noise that’s present at a particular point in the transmission
Typically measured at a receiver Signal-to-noise ratio (SNR, or S/N)
A high SNR means a high-quality signal, low number of required intermediate repeaters
SNR sets upper bound on achievable data rate
power noise
power signallog10)( 10dB SNR
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Shannon Capacity Formula Equation:
Represents theoretical maximum that can be achieved
In practice, only much lower rates achieved Formula assumes white noise (thermal noise) Impulse noise is not accounted for Attenuation distortion or delay distortion not accounted
for
SNR1log2 BC
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Example of Nyquist and Shannon Formulations Spectrum of a channel between 3 MHz and
4 MHz ; SNRdB = 24 dB
Using Shannon’s formula
251SNR
SNRlog10dB 24SNR
MHz 1MHz 3MHz 4
10dB
B
Mbps88102511log10 62
6 C
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Example of Nyquist and Shannon Formulations How many signaling levels are required?
16
log4
log102108
log2
2
266
2
M
M
M
MBC
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TRANSMISSION MEDIA
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Communication Channels
• Wire line Channels (Copper)
• Microwave Radio
• Satellite communication
• Optical Fibre
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Electromagnetic Signal Function of time Can also be expressed as a function of
frequency Signal consists of components of different
frequencies
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Electromagnetic Spectrum
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Classifications of Transmission Media Transmission Medium
Physical path between transmitter and receiver Guided Media
Waves are guided along a solid medium E.g., copper twisted pair, copper coaxial cable, optical
fiber Unguided Media
Provides means of transmission but does not guide electromagnetic signals
Usually referred to as wireless transmission E.g., atmosphere, outer space
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Unguided Media Transmission and reception are achieved by
means of an antenna Configurations for wireless transmission
Directional Omnidirectional
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General Frequency Ranges Microwave frequency range
1 GHz to 40 GHz Directional beams possible Suitable for point-to-point transmission Used for satellite communications
Radio frequency range 30 MHz to 1 GHz Suitable for omnidirectional applications
Infrared frequency range Roughly, 3x1011 to 2x1014 Hz Useful in local point-to-point multipoint applications
within confined areas
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Terrestrial Microwave Description of common microwave antenna
Parabolic "dish", 3 m in diameter Fixed rigidly and focuses a narrow beam Achieves line-of-sight transmission to receiving
antenna Located at substantial heights above ground level
Applications Long haul telecommunications service Short point-to-point links between buildings
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Satellite Microwave Description of communication satellite
Microwave relay station Used to link two or more ground-based microwave
transmitter/receivers Receives transmissions on one frequency band (uplink),
amplifies or repeats the signal, and transmits it on another frequency (downlink)
Applications Television distribution Long-distance telephone transmission Private business networks
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Broadcast Radio Description of broadcast radio antennas
Omnidirectional Antennas not required to be dish-shaped Antennas need not be rigidly mounted to a precise
alignment Applications
Broadcast radio VHF and part of the UHF band; 30 MHZ to 1GHz Covers FM radio and UHF and VHF television
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MULTIPLEXING TECHNIQUES
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Multiplexing Capacity of transmission medium usually
exceeds capacity required for transmission of a single signal
Multiplexing - carrying multiple signals on a single medium More efficient use of transmission medium
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Multiplexing
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Reasons for Widespread Use of Multiplexing Cost per kbps of transmission facility
declines with an increase in the data rate Cost of transmission and receiving
equipment declines with increased data rate Most individual data communicating
devices require relatively modest data rate support
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Multiplexing Techniques Frequency-division multiplexing (FDM)
Takes advantage of the fact that the useful bandwidth of the medium exceeds the required bandwidth of a given signal
Time-division multiplexing (TDM) Takes advantage of the fact that the achievable
bit rate of the medium exceeds the required data rate of a digital signal
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Frequency-division Multiplexing
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FREQUENCY DIVISION MULTIPLEXING
F
R
E
Q
U
E
N
C
Y
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Time-division Multiplexing
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30 CHL PCM MUX FRAME & MULTI FRAME
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 151 MULTI FRMAE (2 m sec)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
FRAME – 125 u sec32 TS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Y 0 0 1 1 0 1 1
Y 1 0 X X X X X
FAW 2
FAW 1
ALTERNATE FRAMES
30 SPCH CHLS
1 = LOSS OF FRAME ALIGNMENT
0 0 0 0 X 0 X X
1 2 3 4 5 6 7 8
FRAMES 1 TO 15
FIRST 4 DIGITS OF FRAME 0 MFAW
DIGIT 1 TO 4 FOR CHL 1 TO 15
SIGNALLING
DIGIT 5 TO 8 FOR CHL 16 TO 30 SIGNALLING 1 = LOSS OF MULTI FRAME
ALIGNMENT
1 2 3 4 5 6 7 8
8 BITS PER CHL
EACH BIT = 488 n sec
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Spectrum & Bandwidth
Spectrum range of frequencies contained in signal
Absolute bandwidth width of spectrum
Effective bandwidth Often just bandwidth Narrow band of frequencies containing most of the
energy DC Component
Component of zero frequency
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WAVE FORM CODING TECHNIQUES
PULSE CODE MODULATION
DIFFERENTIAL PCM
ADAPTIVE DIFFERENTIAL PCM
DELTA MODULATION
ADAPTIVE DELTA MODULATION
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MODULATION TYPES
Modulation is the process of transformation of the message signal (baseband) into a form suitable for transmission over the channel with acceptable degradation.
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• PAM (PULSE AMPLITUDE MODULATION). THE AMPLITUDE OF A TRAIN OF PULSE IS VARIED ACCORDING TO THE AMPLITUDE OF THE ANALOG SIGNAL (MODULATING SIGNAL)
• PCM (PULSE CODE MODULATION). THE ANALOG SIGNAL MODULATES A TRAIN OF PULSE (PAM). IN EFFECT THE ANALOG SIGNAL IS SAMPLED AND THE SAMPLES ARE CODED TO A BINARY VALUE WHICH IS A FUNCTION OF THE AMPLITUDE OF THE SAMPLED ANALOG SIGNAL
Digitizing Analog Speech PAM & PCM
PCM = PAM + QUANTIZATION + COMPANDING
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PULSE CODE MODULATION
• PCM IS A TYPE OF CODING THAT IS CALLED "WAVEFORM" CODING BECAUSE IT CREATES A CODED FORM OF THE ORIGINAL VOICE WAVEFORM.
• PCM IS A WAVEFORM CODING METHOD DEFINED IN THE ITU-T G.711 SPECIFICATION.
• PCM WAS DEVELOPED BY BELL LABS IN 1937
• PCM (ADPCM) IS THE PREFERRED METHOD OF COMMUNICATION WITHIN THE PSTN
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SINGLE CHANNEL SIMPLEX PCM TRANSMISSION SYSTEM
QuantizationCompanding
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PCM BLOCK DIAGRAM
SAMPLINGCIRCUIT
QUANTIZERAND
COMPANDER
ANALOG VOICE
SIGNAL
SAMPLINGCLOCK
PULSE AMPLITUDEMODULATED(PAM) SIGNAL
DIGITIZEDVOICE
SIGNAL
PULSE CODEMODULATED
SIGNAL(PCM)
VOICE BAND FILTER
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PULSE MODULATION
Signal
PAM
PWM
PPM
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SAMPLER QUANTIZER ENCODER
CODEC
Analogsignal
Digitalsignal
• SAMPLING• QUANTIZING• ENCODING
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Pulse Code Modulation(PCM) If a signal is sampled at regular
intervals at a rate higher than twice the highest signal frequency, the samples contain all the information of the original signal (Proof - Stallings appendix 4A)
Voice data limited to below 4000Hz Require 8000 sample per second Analog samples (Pulse Amplitude
Modulation, PAM) Each sample assigned digital value
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SAMPLING THEOREMSTATEMENT :- Any signal with a bandwidth of W can be completely reconstructed if it
is sampled at a rate of 2W.
Original waveform
samples
Capacitor charges
Capacitor discharges
Thus by sampling first at the transmitter and then passing the samples through a LPF the original waveform can be completely reconstructed
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EFFECT OF UNDER SAMPLING
THUS WHEN ANY WAVE IS SAMPLED AT A FREQUENCY THAT IS LESS THAN DOUBLE THE MAXIMUM SIGNAL FREQUENCY, THE RECOVERED WAVE WILL NOT BE OF THE SAME FREQUENCY AS THE INPUT WAVEFORM. THIS DISTORTION IS CALLED ALIASING .
THUS, IT IS SEEN THAT THE SAMPLING FREQUENCY HAS TO BE ADJUSTED SUCH THAT fs > 2fm
ORIGINAL SIGNAL AT 3 Hz SAMPLES AT LESS
SAMPLING RATE AT 2 Hz
WRONGLY RECONSTRUCTED
SIGNAL AT 1 Hz
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Pulse Code Modulation(PCM) 4 bit system gives 16 levels Quantized
Quantizing error or noise Approximations mean it is impossible to
recover original exactly 8 bit sample gives 256 levels Quality comparable with analog
transmission 8000 samples per second of 8 bits each
gives 64kbps
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PULSE CODE MODULATION
IN THIS TYPE OF SOURCE ENCODING THE SPEECH DATA THAT IS SAMPLED IS QUANTISED OR FIXED AT PREDETERMINED LEVELS
IF THE RANGE OF THE INPUT IS -V TO +V THEN, THE ENTIRE RANGE IS DIVIDED INTO STEPS OF 2V/L. THUS THE STEP SIZE IS 2V/L.
IF WE CHOOSE 8 BIT PCM, THEN THE TOTAL No. OF LEVELS ARE 2 = 256 8
IN COMMERCIAL 8 BIT PCM, WE HAVE 256 LEVELS OR 8 BITS PER SAMPLE OF SPEECH DATA. THE SPEECH IS SAMPLED AT THE RATE OF 8 kHz. HENCE THE DATA RATE OF THE COMMUNICATION IS 8 x 8 kHz = 64 kbps
HENCE THE BIT RATE OF EACH SPEECH CHANNEL IN 8 BIT PCM IS 64 kbps
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DIAGRAMMATIC REPRESENTATION OF 3 BIT PCM
0
-4
-3
3
2
1
-1
-2
4
CODE No. 0 -3.5
CODE No. 7 3.5
CODE No. 6 2.5
CODE No. 5 1.5
CODE No. 4 0.5
CODE No. 3 -0.5
CODE No. 2 -1.5
CODE No. 1 -2.5
SAMPLE VALUE 0.0 3.35 1.75 - 0.25 -1.4 -2.3 -3.5
NEAREST Q LEVEL 0.5 3.5 1.5 -0.5 -1.5 -2.5 -3.5
QUANT ERROR +0.5 +0.15 -0.25 +0.25 +0.1 +0.2 0.0
CODE NUMBER 4 7 5 3 2 1 0
ENCODED BITS 100 111 101 011 010 001 000
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LINEAR QUANTIZATION USE OF EQUAL QUANTIZATION INTERVALS THROUGHOUT THE ENTIRE DYNAMIC RANGE OF AN INPUT ANALOG SIGNAL (FOR LOW & HIGH ENERGY SIGNALS) RESULTS IN
LOW LEVEL SIGNALS HAVE A LOW SNR, HIGH LEVEL SIGNALS HAVE A HIGH SNR (UNDESIRABLE)
MOST VOICE SIGNALS ARE OF LOW LEVELS. THUS,VERY INEFFICIENT WAY OF DIGITIZING VOICE SIGNALS TO IMPROVE VOICE QUALITY AT LOWER SIGNALLEVELS, USE A NON-UNIFORM (NON-LINEAR) QUANTIZATION PROCESS CALLED COMPANDING
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NON-LINEAR PCM AND COMPANDING
IT HAS BEEN SEEN THAT SPEECH SIGNALS CONSIST PREDOMINANTLY OF SMALL AMPLITUDE SIGNALS AND THE LARGE AMPLITUDE SIGNALS OCCUR WITH MUCH LESSER PROBABILITY.
HENCE IT IS LOGICAL THAT THE SMALLER AMPLITUDES ARE QUANTISED WITH MORE PRECISION.
THIS MEANS THAT THE STEP SIZE IS MAINTAINED SMALL FOR THE REGION WHERE THE SIGNAL AMPLITUDE IS SMALL. CORRESPONDINGLY, THE STEP SIZE FOR THE LARGE SIGNALS ARE MADE LARGE.
THIS WILL OF COURSE RESULT IN LARGE QUANTISATION ERROR IN CASE OF LARGE SIGNALS. BUT THIS IS TOLERABLE SINCE THE LARGE SIGNAL AMPLITUDES DO NOT OCCUR VERY REGULARLY.
THIS PROCESS OF VARYING THE STEP SIZE DURING THE ENCODING PROCESS IS CALLED COMPRESSING AND THE CORRESPONDING RECEIVER WILL DO EXPANDING TO REVERSE THE DISTORTION INTRODUCED AT THE ENCODER.
THIS PROCESS IS CALLED COMPANDING.
THIS TYPE PCM IS KNOWN AS NON-LINEAR OR LOGRITHMIC PCM
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NON-LINEAR QUANTIZATION
• THE VOLTAGE RANGE BETWEEN THE LOWEST LEVEL AND THE HIGHEST LEVEL IS DIVIDED INTO SEGMENTS IN A NON-LINEAR MANNER
LOGARITHMIC
• THE LOWER THE VOLTAGE LEVELS, THE SMALLER THE RANGE OF A SEGMENT. THE RANGE OF A SEGMENT GETS LARGER FOR HIGHER VOLTAGE LEVELS
• THE NUMBER OF STEPS FOR EACH SEGMENT IS THE SAME
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COMPANDING
• DURING THE COMPANDING PROCESS, INPUT ANALOG SIGNAL SAMPLES ARE COMPRESSED INTO LOGARITHMIC SEGMENTS AND THEN EACH SEGMENT IS QUANTIZED AND CODED USING UNIFORM QUANTIZATION.
• COMPANDING (COMPRESSION AND EXPANSION) INCREASES SNR PERFORMANCE (MINIMISE QUANTIZATION NOISE) WHILE KEEPING THE NUMBER OF BITS USED FOR QUANTIZATION CONSTANT.
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70dB
40dB
30dB
70dB
30dB60dBI/P
60dBO/P
40dB
Compressor Expander80dB
80dB
20dB 20dB
COMPANDOR
A law: Y=Ax /(1+Log A); 0 < V/A
U law: U= log(1+ux) / log(1+u)
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DIFFERENTIAL PCM OR DPCM
IN DPCM THE DIFFERENCE BETWEEN THE PREVIOUS SAMPLE AND THE PRESENT SAMPLE IS ENCODED AND TRANSMITTED.
ONE BIT IS THE SIGN BIT WHICH SAYS WETHER THE PREVIOUS SAMPLE IS MORE OR LESS THAN THE PRESENT SAMPLE AND THREE BITS ARE USED TO ENCODE THE ERROR OR THE DIFFERENCE BETWEEN THE PREVIOUS SAMPLE AND THE PRESENT SAMPLE
ERROR
QUANTISER
INTEGRATOR
DE-QUANTISER
DIFF AMP
BLOCK DIAGRAM OF A DPCM SYSTEM
m(t)
m(t)~
THE ADVANTAGE IN THIS SYSTEM IS THAT, THE DIFFERENCE BETWEEN SAMPLES WILL NOT BE AS LARGE AS THE SAMPLE ITSELF. HENCE, WE CAN USE LESSER NUMBER OF BITS FOR ENCODING. THIS IN TURN REDUCES THE REQUIRED BANDWIDTH.
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0
-4
-3
3
2
1
-1
-2
CODE No. 0 -3.5
CODE No. 7 3.5
CODE No. 6 2.5
CODE No. 5 1.5
CODE No. 4 0.5
CODE No. 3 -0.5
CODE No. 2 -1.5
CODE No. 1 -2.5
DIFFERENCE VALUE +0.5 + 3.0 -1.5 - 1.0 -0.5 -2.0 -1.5
NEAREST Q LEVEL 0.5 3.5 1.5 -0.5 -1.5 -2.5 -3.5
Tx BITS 1001 1111 0011 0010 0001 0100 0011
TRANSMISSIONS IN DPCM
IT MAY BE NOTED THAT EACH STEP IN THIS DPCM IS 0.5V WHEREAS THE STEP SIZE IN THE CORRESPONDING PCM SYSTEM WAS 1V.
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ADAPTIVE DPCM OR ADPCM
IN THIS SYSTEM THE SPEECH WAVEFORM IS PREDICTED AND THE DIFFERENCE BETWEEN THE PREDICTED VALUE AND THE PREVIOUS VALUE IS ENCODED AND SENT.
THE ADVANTAGE OF THIS SYSTEM IS THAT DUE TO PREDICTION THE ERROR MAGNITUDE REDUCES DRASTICALLY AND THUS THE BANDWIDTH ALSO REDUCES CORRESPONDINGLY.
ERROR
QUANTISER
ADAPTIVE PREDICTOR
DE-QUANTISER
DIFF AMP
BLOCK DIAGRAM OF A ADPCM SYSTEM
m(t)~ m(t)
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DELTA MODULATIONIN THE DPCM, THE PCM DATA WAS USED TO PREDICT THE NEXT SAMPLE. FOR TRANSMISSION OF SUCH DATA WE USED ONE SIGN BIT AND THREE INFORMATION BITS. WE CAN DEVISE A NEW SPEECH REPRESENTATION SCHEME WHERE WE CAN SEND ONLY THE SIGN BIT.
WHEN SAMPLED VALUE IS GREATER THAN A REFERENCE THEN A SYMBOL ‘1’
IF THE SAMPLE VALUE IS LESS THEN A SYMBOL ‘0’ IS USED
THIS IS DELTA MODULATION.
PULSE
MOD
UP/DN
COUNTER
D/A CONVERTOR
COMPARATOR
BLOCK DIAGRAM OF A DELTA MODULATOR
m(t)
m(t)~
V(n) = +1 if m(t) >= m(t)~
V(n) = -1 if m(t) < m(t)~
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GRAPHICAL REPRESENTATION OF DELTA MODULATION
AND THE PROBLEMS THEREIN
m(t)
m(t)~
SLOPE
OVERLOAD
PROBLEM DUE TO SMALL STEP SIZE
time
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PROBLEMS IN DELTA MODULATIONTHE MAJOR PROBLEMS OF DELTA MODULATION ARE :-
(a) SLOPE OVERLOAD WHICH RESULTS WHEN THE SLOPE OF THE SIGNAL EXCEEDS THE SLOPE OF THE DELTA MODULATOR. THIS PROBLEM CAN BE OVERCOME BY USE OF A LARGE STEP SIZE.
(b) SMALL SIGNAL VARIATIONS OF THE SIGNAL RESULT IN ALTERNATE 1’s AND 0’s WHICH DURING RECONSTRUCTION, WILL RESULT IN A dc LIKE SIGNAL. THIS PROBLEM CAN BE OVERCOME BY USE OF A SMALL STEP SIZE.
THESE CONFLICTING DEMANDS OF A LARGE STEP SIZE AND SMALL STEP SIZE CAN BE OVERCOME BY USE OF SPECIAL DELTA MODULATOR WHICH
- USES A SMALL STEP SIZE WHEN THE SIGNAL VARIATIONS ARE SMALL
- USES A LARGE STEP SIZE WHEN THE SIGNAL VARIATIONS ARE LARGE
SUCH A SYSTEM IS CALLED THE ADAPTIVE DELTA MODULATOR OR ADM
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DIFFERENCE
AMPLIFIERMODULATOR
PULSE
GENERATOR
INTEGRATORVARIABLE GAIN AMP
SQUARE LAW
DEVICE
m(t)~
m(t)
BLOCK DIAGRAM OF ADAPTIVE DELTA MODULATOR
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VARIABLE STEP SIZE OF ADM
ACTUAL WAVEFORM
DM OUTPUT
VARIABLE STEP SIZE AT THE INPUT OF THE
INTEGRATOR
THUS IT CAN BE SEEN THAT THE ADM OUTPUT IS ABLE TO FOLLOW THE ACTUAL SPEECH WAVEFORM MUCH MORE CLOSELY THAN THE DM OUTPUT WHICH IS SEVERELY AFFECTED BY SLOPE OVERLOAD
THE ADM OUTPUT IS “ 1 0 1 1 1 1 1 0 1 0 1 0 1 0 ”
1 0
11
1
1
1
1
0 00
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Relationship between Data Rate and Bandwidth
The greater the bandwidth, the higher the information-carrying capacity
Conclusions Any digital waveform will have infinite
bandwidth BUT the transmission system will limit the
bandwidth that can be transmitted AND, for any given medium, the greater the
bandwidth transmitted, the greater the cost HOWEVER, limiting the bandwidth creates
distortions
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POWER MEASUREMENTS
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UNITS OF MEASUREMENT
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UNITS OF MEASUREMENT THE POWER LEVEL IN TRANSMISSION
EQUIPMENTS ARE VERY SMALL TO VERY BIG.
IF ALL THE MEASUREMENTS ARE TAKEN HAVING THE SAME IMPEDANCE THE VOLTAGE WILL GIVE DIRECT INDICATION OF THE POWER LEVEL
RIP
REP
*2
2 /
EIP
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THE DECIBEL The decibel is widely used in
transmission system The decibel is a unit that
describes a ratio. It is logarithmic with base 10
dB = 10 log (P2/P1)Where P1is input level & P2 is
output level
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dB
Gain (dB)=10 log (output/input) = 10 log 2/1
= 10(0.30103) = 3.0103 approximately 3 dB gain
Net work1W 2W
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dBRATIO dB2 3
3 5
10 10
4 = 2*2 ?
5 = 10/2 ?
80 = 2*2*2*10
?
500 = 5*1001000/2
?
.001=1/1000 ?0.02 = 2/100 ?
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dBRATIO dB
2 3
3 5
10 10
4 = 2*2 3+3 = 6
5 = 10/2 10 – 3 =7
80 = 2*2*2*10 3+3+3+10 = 19
500 = 5*1001000/2
7 +20 = 2730 – 3 =27
.001 = 1/1000 – 30
0.02 = 2/100 3 - 20 =-17
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dBRATIO dB10 10100 201000 3010,000 400.1 -100.01 -200.001 -300.0001 -40
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BASIC DERIVED DECIBEL UNIT
1. dBm : Power level related to 1 mW
Power (dBm) = 10 log (Power in mW/1mW)
Eg. 20 W power = 10 log (20*1000/1)
= + 43 dBm2. dbw: dBW= 10 log power (w)/1w +30 dBm = 0dBW
-30 dBW = 0dBm dBW = dBm +30 dB
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CORRECTION FACTOR Most instrument have internal
impedance of 600 . If the impedance of circuit under test is 600 , then reading will be correct. If the circuit impedance is 150 then,Indicated Power =
Actual power =
Error =Error in dB =
dB
EE
EE
E
E
6)600/150log(10
)150/log(10)600/log(10
)150/()600/(
150/
600/
22
22
2
2
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CORRECTION FACTOR Thus the correction factor =
+6 dB
The correction factor for 300 is ?
For 75 impedance it is ?
+3dB
+9dB
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EXERCISE
-12dB +35 dB -10dB4 mw ?
Net work 27 dB loss
Network 27 dB gain
1 w ?
10 w ?
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ZERO TRANSMISSION LEVEL POINT (ZTLP) ZTLP – it is the point in the system
at which the standard test tone has an absolute power of 1mw or 0 dBm
It is a reference level for the system
Generally situated in the trunk exchange at the transmit end of a long haul system
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RELATIVE TRANSMISSION LEVEL(dBr) The level of any point in the
system expressed in dB relative to ZTLP is referred to as dBr of that point
E.g. –33 dBr point in the system will be 33 dB below the ZTLP
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RELATIVE POWER LEVEL(dBmo) The term dBmo is a measure of power
at any dBr point with reference to 0 dBm at the ZTLP
dBmo = dBm - dBr E. g. A tone of +36 dBm measured at
+19 dBr transmission level point is equivalent to +17 dBmo
A tone of +17 dBmo is equivalent to +7 dBm measured at – 10 dBr point
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NOISE MEASURING UNITS The interfering effect of noise on
speech telephony is a function of response of human ear to specific frequencies in the voice channel
1000Hz tone at –90 dBm was chosen as reference
Any level below -90 is not ordinarily audible
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dBrn Western electric 144 hand set used 1KHz at –90 dBm taken as
reference 0 dBrn = -90 dBm at 1000 Hz
+90 dBrn = 0 dBm or 1 mW Weighing net work provides 8 dB
attenuation at 3KHz band of white noise
dBrn = dBm + 82 for white noise of 3 KHz
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dBa dBa – stand for dB reference noise
adjusted Western electric w-3 type F1-A hand
set used 1000 Hz at –85 dBm taken as
reference0 dBa = - 85 dBm at 1KHz
Weighing net work provides 3 dB attenuation when subjected to 3 KHz band of white noise
dBa = dBrn – 5 for 1KHz tone= dBm +82 for white noise of 3 KHz band
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dBrnc Western electric type 150 hand set used 1000Hz at – 90 dBm taken as reference
0 dBrnc = - 90 dBm at 1000 Hz Weighing net work provides 2 dB
attenuation at 3KHz band, also known as message weighing
dBrnc = dBrn, dBa – 5 for single tone of 1KHz
= dBrn +6, dBa +6, dBm + 88 for white Noise of 3 KHz band
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dBmp & pWp It is measured with psophometer &
called psophometrically weighted 800 Hz at 0 dBm taken as reference Provides 2 dB attenuation at 3KHz band
0 dBmp = 0 dBm at 800 Hz
=dBm – 2 for white noise of 3 KHz