1 an najah national university telecommunication engineering department digital communications 69342...
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1
An Najah National UniversityTelecommunication Engineering
Department
Digital Communications69342
TDM
Dr. Allam Mousa
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3.9 Time Division Multiplexing (TDM)
LPF
LPF
LPF
LPF
Pulse modulator
Commuchannel
Pulse demod
LPF
LPF
LPF
Message 1
Message N
Message 3
Message 2
Low-Pass anti alliasing Filter
commulator De Commulator
Low-Pass reconstruction
Filter
Message Output
1
N
2
Multiplexed signal
Clock pulse
Clock pulse
synchronized
Block diagram of TDM
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1)The commulator
1-Takes a narrow sample of each of the N signals at a rate fs>2W.
2-Sequentially interleave these N samples inside the sampling interval Ts .
TDM Bandwidth expansion factor N.
2) Pulse modulator
Transfers the multiplexed signal into a form suitable for transmission over the communication channel.
3)Pulse demodulator +Decommulator
Frame Ts
S11 S21 S31 S41 S51 S12 S22 S32 S42 S52
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Synchronization
For PCM. System
As the number of signals to be TDM increases, the duration of a codeword representing a single sample is reduced. Hence pulse duration is reduced. So it is more difficult for generate or transmit.
For short pulses, we have more noise in the Tx media .
So, we have a restricted number of signals to be TDM .
The time operation at the Rx follow closely the time operation at the Tx. (except for transmission time…)
To synchronize the Tx + Rx.
Set a pulse at the end of a frame and transmit this pulse every other frame only .
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Example (The T1 System (a PCM system)
TDM system is given such that:
N=24 Voice channels (300-3100) Hz.
Repeaters at 2 Km intervals.
LPF with fc=3.1KHz
fs=8KHz .
8 bit / sample
mu-law (mu=255)
1)Find the frame length.
2)Find the number of bits/frame.
3)Find the number of bits/second.
4)Find the duration of each bit.
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Solution :
1) fs = 8KHz Ts=1/ fs=1/8000=125 µs (Ts is the frame length)
2) 24 Samples + 1 bit for synch 24(8) + 1=193 bits/frame .
3) 193 bits 125 µs 193 bits * 1 sec = 1.544Mb/s
??? 1 s 125 µs
4) 193 bits 125 µs 125 µs * 1 bit =0.647 Ms
1 bit ??? 193 bit
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3.10 Digital MultiplexersTDM is used to multiplex a group of analog signals after sampling them in time at a common (same) sampling rate .
If we have digital signals (with different bit rates) and we need to combine them into a single data stream (at a considerably higher bit rate than any of the inputs ) then we use a bit-by-bit interleaving procedure [digital multiplexing].
Multiplexer
High-speed Transmission
lineDemultiplexer
1
2
N
1
2
N
Fig-diagram of a digital multiplexing - demultiplexing
bit-by-bit interleaving procedure.7 Sec_2_TDM
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Digital Multiplexer are used to : (CHECK?)
1)Take relative low bit rate data streams from digital computers and multiplex them for TDM transmission over the public telephone network (using modems).
2)Data transmission services.
Digital Signal Zero (DSO) is the incoming signals with 64Kbps rate .
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TDM PCM
PCM
PCM
PCM
TDM
m1(t)
m2(t)
mN(t)
m1(t)
m2(t)
mN(t)
Byte interleaved TDM .
Analog Multiplixing followed by PCM
Bit interleaved TDM
PCM followed by digital multiplexing
Categories Digital Multiplexing 9
(CHECK?)
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Digital TDM Hierarchy (The North America Standard) .
DS0 : Digital Signaling Zero where the incoming signal has a 64kp/s rate (PCM).
DS1 : Digital Signal one, it combines 24 DS0 bit stream to get 1.544Mb/s >(24(64)).
DS2 : Combines 4-DS1 bit streams to obtain a 6.312 Mb/s >(4(1.544)).
DS3 : Combines 7-DS2 bit streams to obtain a 44.736Mb/s >(7(6.312)).
DS4 : combines 6-DS3 bit streams to obtain a 274.176Mb/s >6(44.736)).
DS5 : combines 2-DS4 bit streams to obtain a 560.160Mb/s > 2(274.176).
Due to bit stuffing, he bit rate of a digital signaling produced by any of these multiplexers is slightly higher than the prescribed multiple of the incoming bit rate (i.e., DS1 =1.544 which is greater than 24*64)
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3.11 Virtues, Limitations and Modifications of PCM .
PCM main advantage is the use of “Coded Pulses for the digital representation of analog signals”
Advantages:
1)Robustness to channel noise & interference .
2)Efficient regeneration of the coded signal a long the transmission path .
3)Efficient exchange of increasing channel B.W for improved SNR, obeying an exponential law.
4)A uniform format for the transmission of different kinds of baseband signals.
5)Easy to drop or reinsert a source in the TDM system .
6)Secure Communication through the use of special modulation scheme or encryption.
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Disadvantages :
1)Increased system complexity.
2)Increased channel B.W .
These are not serious any more as;
1) DM is simpler than PCM to be implemented .
2) VLSI are cheaper than before. {implementation is not a problem}.
3)PCM requires B.W. This may be solved as:
I) Fiber optics & satellite channels have very large B.W .
II) Using Data compression techniques removes redundancy from PCM. So reducing the bit rate of the transmitted data without serious degradation in system performance .
Reducing bit rate increasing the security or complexity or…
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3.12 Delta Modulation (DM)The incoming signal is over sampled (fsample >>fNyquist). This is to increase the correlation between adjacent samples of the signal.
Binary
Sequence
at modulator
Output
0
00
00
11
11
10
1
1
1 00
00
00
)t(Ts
Star case approximation mq (t)
The difference between the input & the approximation is quantized into only two levels. ,+_
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DM provides a stair case approximation of the over sampled signal
Let : m[n] = m(nTs) n=0,1,2,3... & Ts is sampling period . (n positive or negative).
e[n] =m[n] –mq[n-1] error signal . m[n] : present sample .
mq[n-1] : latest approximation
eq[n] = sgn (e[n]) quantized version of e[n] .
mq[n] = mq[n-1] + eq[n] signum function
The quantizer output eq[n], is coded to produce the DM signal .
The rate of information transmission = sampling rate fs = 1/Ts .
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One- bitQuantizer
Z
LPFDecoder
Z
Encoder
-1
++
+
+
Sampled Message
Signal m[n]
DM
WAVE
DM – Transmitter
-1 DM – Receiver
Sampled
Channel output
+
+-
++
Accumulator
Accumulator
e[n] eq[n]
mq[n]
mq[n-1]
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Fig. DM Transmitter AND DM Receiver
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DM – quantization errors
1) Slope over load distortion.
2) Granular noise.
mq[n] =m[n] + q[n] .
but , e[n] = m[n] – m[n-1] – q[n-1] .
granular noise.
is too large relative to the local slop
of m(t)
Strain case approximation
mq(t)
Ts
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In order for the sequence of samples mq[n] to increase as fast as the input sequence of samples mq[n] in a region of maximum slope of m(t) , the following condition must be satisfied ,
/ Ts >=max dm(t / dt
Other wise is too small for the stair case approximation .
granular noise occurs when is too large & it is similar to quantization noise in PCM .
The Solution is Adaptive Delta Size (ADM)
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Delta – Sigma Modulation
In DM noise result in an accumulative error in the demodulated signal ,
This draw back can be over come by integrating the message signal prior to DM.
Advantages of the integrator :
1) Low frequency content of the input signal is pre-emphasized .
2) Correlation between adjacent samples of the DM input is increased
3)Simplifies the design of Rx .
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LPF
Pulse generator
+
+
Comparator
Integrator 1
Integrator 2Tx
Hard limited
Pulse modulator
Message signal m(t)
Estimaete of message signal
Rx
Delta – Sigma modulation : may also be clled Sigma – Delta Modulation because Sigma (integration) is performed before Delta Modulation .
Delta – Sigma Modulation
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PCM Bandwidth requirements .
q quantization levels are used
q= 2^n n : # of bits
n = log q , binary pulses must be transmitted to represent each sample of the
signal.
If the signal has a bandwidth of W & sampling rate fs=2W Then,
2nW binary pulses (bits) must be transmitted / sec. {depending on format}
1 sample has n bits
2 W sample ???
(n bits *2W sample)/ (1 sample) = 2nW bits /sec is the data rate.
2
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Small error requires large B.W .
Error is exchanged with bandwidth .
B.W =1/T = 2nW for Unipolar NRZ
=knW for some other forms.
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Max. width of each binary pulse is Tmax = 1/(2nW)
Bandwidth (B) = 1/T= 2nW .
In general, knW is the Bandwidth depending on the line coding method .(required Bandwidth)
B =2W log q lower bound on B.W .
2
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3.13 Linear PredictionFinite – duration Impulse Response (FIR) discrete – time filter .
Z-1
Z Z Z-1 -1 -1
W1 W2 W3 Wp-1 Wp
X[n-2]
X[n]
X[n-1] X[n-3] X[n-p+1] X[n-p]input
Block of Linear Prediction filter of order P Prediction X[n] ^
X[n] = X[n-1]W1 + X[n-2]W2 + X[n-3]W3 + ………….+ X[n-p]Wp..^
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1) P: Prediction order (i.e., # of units – delay .
2) e[n] = X[n] – X[n] , prediction error .
The design objective is to choose the filter coefficients W1 ,W2, W3, …..,Wp , Such as to minimize an index of performance (J).
3) J = E[e [n] ] . Sub. 1 & 2 into 3 leads to
4) J = E [X [n] ] – 2 Wk E[ X [n] ] X [n-k] ] + Wj Wk E[ X [n-j] X[n-k] ]
Assume X(t) has a zero mean ( i.e., X(t) is a stationary process), then
E[ X [n] ] = 0 for all n
2
2
X[n] = Wk X [n-k]
pp p
p
j=1
k=1
k=1
k=1
^
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Define ,
σx : variance of a sample of the process X(t) at nTs = E [X [n] ] ..
• Rx(kTs) : auto correlation at the process X(t) for a lag of kTs = Rx [k]
• =E[x[n] x[n-k]]
• So ,
• J =σx
2 2
2
ΣWj Rx [k – j]=Rx [k] = Rx [-k] , k = 1,2,3…….P
Optimal equations j=1
P
Wiener – Hopf equations for linear prediction.
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In matrix form, Let W = [ W1 W2 ……Wp ] , optimum coefficients vector .Px1
T
o
rx = [Rx [1] Rx[2] ………..Rx[p] ] , autocorrelation vector Px1
Rx =
Rx[0] Rx[1]…………. Rx[p-1]
Rx[1] Rx[0] ………….Rx[p-2]
Rx[2] Rx[1] ………….Rx[p-3]
Rx[p-1] Rx[p-2] ………Rx[0]
Wiener – Hopf eqs ,can be written as :
optimum solution.
Rx Wo = rx Wo = R rx -1
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Linear Adaptive predictive
Wo = Rx rx requires knowledge of the autocorrelation function Rx [k] , k= 0,1,2,…….., P
What if Rx [k] is not a available ???
Solution : Use the “ adaptive prediction “ + recursive methods .
Linear predictor
Wk [n] Z
+
-1
^ ^
+ -
Input X[n]Prediction
X[n]
Error e[n]
Block diagram linear Adaptive prediction process
Least Mean Square LMS
Mean Square Error MSE
LMS
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3.14 Differential Pulse Code Modulation (DPCM)
fs >>fN highly correlated samples .
highly correlated
samples PCM Encoded signal with redundant information
Symbols that are not essential to the transmission are generated as a result of
PCM encoding
Removing the redundancy before encoding more efficient coded signal
DPCM Depends on Linear Prediction.
Wk m[n-k] = m[n] ∑P
K=1
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LPF SAMPLER ENCODERQUANTIZER
REGENE DECODERLPF
reconstDistination
m(t)
PCM
Applied to channel input
PCM
Quantizer Encoder
decoder
Prediction filter
prediction
input
Sampled input m[n]
DPCM
Wave
Fig. DPCM Tx
Fig. DPCM Rx++
+
++
-
eq[n] e[n]
m[n]^
mq[n]
mq[n]=m[n]+eq[n]^
eq[n]=e[n]+q[n]
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e[n] = m[n] – m[n]
eq[n] = e[n] + q[n]
mq[n] = m[n] + eq[n]
= m[m] + e[n]+ q[n]
mq[n] = m[n] + q[n] mq[n] is the quantize version of the input signal .
q[n] can be +
^
^
^
-
The prediction filter in the Tx & Rx operate on the same sequence of samples , mq[n] . So we have a feedback path added to the quantizer in the Tx .
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The variance of the prediction error e[n] is smaller than the variance of the m[n],so we have a smaller quantization error.
m[n] mq [n]
OR e[n] eq [n].
Q
Q
m[n] e[n] eq [n]Quantizer (DPCM)
OR
One bit Q (DM)
Encoder
Prediction filter
OR
Z^-1 ( DM)
mq [n]
+
-
+
+
mh[n]
OR
mq[n-1] (DM)
DPCM
OR
DM
Comparing
DM with DPCM
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So, DM is a special case of DPCM BUT
1) DM uses one –bit (two-level) quantizer.
2) DM prediction filter is a signal delay element (zero prediction order).
DM and DPCM Transmitters use feedback but PCM does not.
DM and DPCM are subject to slope-over load distortion .
PCM and DPCM suffers from quantization noise.
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Progressing gain :
DPCM m[n] DPCM
)SNR(O= σM/ σQ σ M: variance of the original input sample m[n].
σQ : variance of the quantizatin erroe q[n].
)SNR(O= σM/ σQ = (σM/ σE )(σE/ σQ ) = Gp (SNR)Q σE :variance of the prediction error.
Where
)SNR(Q=( σE/ σQ )
GP = (σM/ σE )
Gp > 1 Gain in SNR due to DPCM.
Gp is Maximized by minimizing σE (aim of LP Filter design ).
10 log (SNR)O=1.8+6R
2
2
2
2 2
2 2
2 2
2 22 2 22
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3.15 Adaptive Differential Pulse Code Modulation (ADPCM)
Standard PCM 64 kb/s HENCE, large B.W is required .
To reduce bit rate, we can use coding :
1) Remove redundancies from the signal (speech) as far as possible.
2) Assign the available bits to code the non redundant parts of the signal (speech) in a perceptually efficient manner .
Reducing bit rate increasing the complexity .
ADPCM 32kb/s adaptive quantization .
adaptive prediction.
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Adaptive Quantization : quantizer with time varying step size [n].
] n = [Ø σ [n] estimate of the standard deviation σ [n]
Constant.
To implement [n]= Ø σ [n]:
1) Adaptive Quantization with forward estimation (AQE) :
Unquantized samples of the input signal are used to derive forward estimates of σ [n] .
2) Adaptive Quantization with backward estimation (AQB) :
Unquantized samples of the input signal are used to derive backward estimates of σ [n].
M
n
M
M
n
M
M
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Table Encoding techniques applied to speech signals.
Encoding method Quantizer Coder(bits) Transmission rate (bits /sec )
PCM linear 12 (8) 96 64
Log PCM logarithamic 7-8 (8) 56 – 64 64
DPCM logarithamic 4-6 (4) 32 – 48 32
ADPCM Adaptive 3-4 (4) 24 – 32 32
DM binary 1 32 – 64 32
ADM adaptive binary 1 16 -32 16
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Computer Experiment: Adaptive Delta Modulation
In DM ,
1) If successive errors are of opposite polarity, DM is in the granular mode, Reduce the step size
.
2) if successive errors are of the same polarity , DM is in the slop – over load mode , increase the step size
D 2D, or 3D or 4D,…
OR
D Dmin
Delta adaptation
NEED the eqution
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3.17 MPEG Audio Coding Standard
Speech (voice) and Audio are similar in that the quality of a coding scheme is based on the properties of human auditory perception.
Speech speech production model is available so we have an efficient coding scheme (ADPCM).
Audio No production model is available .
MPEG-1 : Motion Picture Expert Group 1 .
MPEG-1/audio coding standard is a lossy compression system [like ADPCM] .
BUT it can achieve transparent, perceptually, lossless compression of stereophonic audio signals at high sampling rate.
Mean Opinion Score (MOS) test is used by MPEG committee with 6-to-1 compression ratio is good (indistinguishable) .
(original and coded audio signals are indistinguishable).
This is due to the usage of the characteristics of the human auditory system
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1) Critical bands ( in the inner ear ).
20 kHz is the band .
20kHz
Filter banks 25 filters over lapping with frequencies from 100Hz up to 5kHz .
2) Auditory Masking : when low signal (maskee) and a high level signal (masker) occur simultaneously and close enough to each other in frequency.
38
masking threshold
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