pulse code modulation (pcm). example solution in the previous example we have 8-quantization levels...
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![Page 1: Pulse Code Modulation (PCM). Example Solution In the previous example we have 8-quantization levels (to encode with 3-bits) from code number 0 to 7 (from](https://reader035.vdocuments.mx/reader035/viewer/2022062720/56649eff5503460f94c1545c/html5/thumbnails/1.jpg)
Pulse Code Modulation (PCM)
![Page 2: Pulse Code Modulation (PCM). Example Solution In the previous example we have 8-quantization levels (to encode with 3-bits) from code number 0 to 7 (from](https://reader035.vdocuments.mx/reader035/viewer/2022062720/56649eff5503460f94c1545c/html5/thumbnails/2.jpg)
Example
0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3
3.5
m(t)
m(t)
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Solution
In the previous example we have 8-quantization levels (to encode with 3-bits) from code number 0 to 7 (from binary code 000 to 111)
Sample value: 2.8 3.2 2.7 1.1 Nearest level: 3 3 2.5 1Code number: 6 6 5 2Binary code: 110 110 101 010
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![Page 5: Pulse Code Modulation (PCM). Example Solution In the previous example we have 8-quantization levels (to encode with 3-bits) from code number 0 to 7 (from](https://reader035.vdocuments.mx/reader035/viewer/2022062720/56649eff5503460f94c1545c/html5/thumbnails/5.jpg)
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PCM Transmitter Block Diagram
L
r=nfs
n
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n:
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PCM transmitter
n
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PCM transmission path
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The most important feature of PCM systems is the ability to control the effects of distortion and noise. A PCM signal may be reconstructed from the distorted and noisy input by means of regenerative repeaters placed sufficiently close to each other along the transmission route
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Transmission Bandwidth of a PCM Wave
• Each encoded message sample is represented by a n-digit code word.Consequently, the signal bit rate (r) becomes
r = n fs fs ≥ 2 W, Where:
W= The message B.W. , fs= Sampling rate
• The transmission bandwidth (BT) required by the PCM wave is:
nWnfrBsT
2
1
2
1
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Main feature of pulse-code modulation
• If the regenerators are well placed then they cancel the effect of channel distortion and noise.
• In this case the only source of distortion and noise is the quantization error
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Time-Division Multiplexing(TDM)
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Ts
Tx
For exampleWe multiplex two signals g1(t), and g2(t)
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TDM: - Multiple data streams are sent in different time in single data link/medium - Data rate of the link must be larger than a sum of the multiple streams - Data streams take turn to transmit in a short interval - widely used in digital communication networks
A
B
C
A
B
C
MUX
DEMUX
… A1 B1 C1 A2 B2 C2 …
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TDM: Concept of Framing and Synchronization
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DefineTs = sampling interval (period)
fs = sampling frequency (rate)
Tx = time spacing between adjacent samples in the TDM signal waveform
• Consider two cases: Equally sampled ( N of input signals ) Tx = Ts / N N : number of samples Non equally sampled Signals have non equal bandwidths
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Minimum Bandwidth
• The resultant signal could be considered as a new one sampled with fx . To get the B.W. of the TDM-PAM signal:
• The used system must have a minimum B.W. equals to fx / 2 in order to pass the TDM-PAM signal.
• The B.W = K fx (½) < K < 1
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Equally sampled signals• Example-2
Two signals each band-limited to W = 3 KHz N = 2 signals• Ts = 1 / ( 2W) = ( 6000)-1 = 166.7 μ sec.
• Tx = Ts / 2 = 83.3 μ sec.
• B ≥ ( 1 / 2Tx ) ≥ 6 KHz
• N.B. PAM is as efficient in conserving bandwidth as SSB when all the signals have the same bandwidth.
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• Example-3If we have 20 signals each band-limited to 3.3
KHz sampled with rate 8 KHz and PAM-TDM is used. Find the min. clock freq. and min. B.W.
Solution:Clock frequency fx=8K20=160 KHz
Min. B.W.=fx/2 =80 KHz
If PCM-TDM is used using 3-bits/sample:The bit rate = 8K 203 = 480 Kb/s
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Non-equally sampled signals
• For signals having non equal bandwidths we do non equal sampling
• To conserve B.W. PAM time multiplexed systems usually group input signals of comparable bandwidths
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• Example three signals band limited to W , W and 2W
Equally Sampled:• fs = 4 W
• Ts = 1 / 4 W
• Tx = 1 / 12 W
• fx = 12 W
• B = fx/2 = 6 W
> SSB B.W.
number Of
samplesfs
B.W Signal
1 2W W S1
1 2W W S2
1 4W 2W S3
3 1 2 3
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Non equally sampled• Ts = 1 / 2W• N = 4• Tx = 1/(8W)• B = 4W• = SSB B.W.
number of
samplesfs B.W Signal
1 2W W S1
1 2W W S2
2 4W 2W S3
1 3 2 3 1
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1.544Mb/s
T1
44.736 Mb/s
T3
PCM
Mux
12
24
M12
Mux
1
2
4
6.312 Mb/s
T2 M23
Mux
12
7
M34
Mux
1
2
6
274.176 Mb/s
North American Digital Hierarchy
EXAMPLE OF NON EQUALLY SAMPLING T1– DIGITAL SYSTEM
T4
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Multiplexing PCM signals
• 24 – analog signals each band-limited to 3.3 K sampled at a rate of 8 K. Frame time=125 s
• At 6000 ft, repeaters are used• Each sample is encoded by 8-bits• No. of levels = 256 level• No. of bits /frame = (24 8) + 1F bit = 193 bitsWhere: 1F is one frame synchronization bit• Bit rate for T1 channel =(193 8K)=1.544 Mb/s
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T1 TDM format for one frame.
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Multiplexing T1-Lines
• 4-T1 lines are multiplexed to generate one T2 line.
• M12 multiplexer adds 17 bits for synch.
• Number of bits/frame = (193 4) + 17 = 789 bits/frame• Bit rate for T2 =789 8K = 6.312 Mb/s
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Multiplexing T2-Lines
• 7-T2 lines are multiplexed to generate one T3 line.
• M23 multiplexer adds 69 bits for synch.
• Number of bits/frame = (789 7) + 69 = 5592 bits/frame• Bit rate for T3 = 5592 8K = 44.736 Mb/s
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Multiplexing T3-Lines
• 6-T3 lines are multiplexed to generate one T4 line.
• M34 multiplexer adds 720 bits for synch.
• Number of bits/frame = (5592 6) + 720 = 34272 bits/frame• Bit rate for T4 = 34272 8K = 274.176 Mb/s
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Line Coding
• How to represent the ‘1’ and ‘0’
• Each line code has its advantage and disadvantage
• A good line code should have the following requirements:
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Requirements of line code:
• Transmission bandwidth : as small as possible• Error detection and correction• Avoid D.C. ( due to the A.C. coupling used at the
repeaters• Adequate timing content: It should be possible
to extract timing or clock information from the signal
• (long sequence of zeroes could cause errors in timing extraction for certain line codes)
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Line Codes
1
1
1
1
1
1
0
0
0
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Examples
• On/Off (unipolar)– “1” send p(t), “0” nothing – Return to zero (RZ)– Non-Return to Zero (NRZ)
• Polar (bipolar)– “1” send p(t), “0” send -p(t) Bipolar (RZ) Bipolar (NRZ)
1 1 1 0 0 1 1
1 1 1 0 0 1 1
1 1 1 0 0 1 1 1 1 1 0 0 1 1
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• Bipolar Alternate Mark Inversion (AMI):
– “0” has no pulse– “1” changes the sign of the waveform p(t)
1 1 1 0 0 1 1
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• Bi-phase Codes (Manchester)
• More complex waveforms can “split” the phase of the two signals
1 1 1 0 0 1 1