4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part...
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Transcript of 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part...
![Page 1: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/1.jpg)
4.2 Digital Transmission
Outlines
□ Pulse Modulation (Part 2.1)□ Pulse Code Modulation (Part 2.2)□ Delta Modulation (Part 2.3)□ Line Codes (Part 2.4)
![Page 2: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/2.jpg)
□Basic scheme of PCM system□Quantization□Quantization Error□Companding□Block diagram & function of TDM-PCM
communication system
![Page 3: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/3.jpg)
Basic scheme of PCM system
□The most common technique for using digital signals to encode analog data is PCM.
□Example: To transfer analog voice signals off a local loop to digital end office within the phone system, one uses a codec.
![Page 4: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/4.jpg)
Cont’d...
□Because voice data limited to frequencies below 4000 Hz, a codec makes 8000 samples/sec. (i.e., 125 microsecond/sample).
□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.
![Page 5: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/5.jpg)
PCM Block Diagram
• Most common form of analog to digital modulation• Four step process
1. Signal is sampled using PAM (Sample)2. Integer values assigned to signal (PAM)3. Values converted to binary (Quantized)4. Signal is digitally encoded for
transmission (Encoded)
![Page 6: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/6.jpg)
4 Steps Process
![Page 7: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/7.jpg)
Cont’d…□ Analog signal is sampled.□ Converted to discrete-time continuous-amplitude signal (Pulse Amplitude Modulation)
□ Pulses are quantized and assigned a digital value.□ A 7-bit sample allows 128 quantizing levels.
□ PCM uses non-linear encoding, i.e., amplitude spacing of levels is non-linear□ There is a greater number of quantizing steps for low amplitude□ This reduces overall signal distortion.
□ This introduces quantizing error (or noise).□ PCM pulses are then encoded into a digital bit stream.□ 8000 samples/sec x 7 bits/sample = 56 Kbps for a single voice
channel.
![Page 8: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/8.jpg)
PCM Example
![Page 9: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/9.jpg)
Quantization
□ A process of converting an infinite number of possibilities to a finite number of conditions (rounding off the amplitudes of flat-top samples to a manageable number of levels).
![Page 10: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/10.jpg)
Cont’d...
Analog input signal
Sample pulse
PAM signal
PCM code
![Page 11: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/11.jpg)
The quantization interval @ quantum = the magnitude difference between adjacent steps.
The resolution = the magnitude of a quantum = the voltage of the minimum step size.
The quantization error = the quantization noise = ½ quantum = (orig. sample voltage – quantize
level)
PCM code = (sample voltage/resolution)
Cont’d…
![Page 12: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/12.jpg)
□ A difference between the exact value of the analog signal & the nearest quantization level.
QUANTIZATION ERROR
![Page 13: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/13.jpg)
Types of Quantization
Midtread Midrise
![Page 14: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/14.jpg)
Types of Quantizer1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.
![Page 15: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/15.jpg)
Dynamic Range (DR)
□ Largest possible magnitude/smallest possible magnitude.
□ Where □ DR = absolute value of dynamic range□ Vmax = the maximum voltage magnitude□ Vmin = the quantum value (resolution)□ n = number of bits in the PCM code
resolution
V
V
VDR max
min
max
12 nDR
)log(20)( DRdBDR
![Page 16: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/16.jpg)
Example 1
1. Calculate the dynamic range for a linear PCM system using 16-bit quantizing.
2. Calculate the number of bits in PCM code if the DR = 192.6 dB
![Page 17: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/17.jpg)
Coding Efficiency
□A numerical indication of how efficiently a PCM code is utilized.
□The ratio of the minimum number of bits required to achieve a certain dynamic range to the actual number of PCM bits used.
Coding Efficiency = Minimum number of bits x 100
Actual number of bits
![Page 18: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/18.jpg)
Signal to Quantization Noise Ratio (SQR)
□ The worst-case voltage SQR
□ SQR for a maximum input signal
□ The signal power-to-quantizing noise power ratio
eQ
resolutionSQR (min)
eQ
VSQR max
(max)
12
2
12
)(
22
2
log10)(
log10
power noiseon quantizati average
power signal averagelog10
Rv
dB
v
R
SQR
R =resistance (ohm)
v = rms signal voltage
q = quantization interval
![Page 19: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/19.jpg)
Example 2
1. Calculate the SQR (dB) if the input signal = 2 Vrms and the quantization noise magnitudes = 0.02 V.
2. Determine the voltage of the input signals if the SQR = 36.82 dB and q =0.2 V.
![Page 20: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/20.jpg)
Effect of Non-Linear Coding
![Page 21: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/21.jpg)
Nonlinear Encoding
□ Quantization levels not evenly spaced
□ Reduces overall signal distortion
□ Can also be done by companding
![Page 22: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/22.jpg)
Companding
• The process of compressing and then expanding.• The higher amplitude analog signals are compressed
prior to transmission and then expanded in receiver.• Improving the DR of a communication system.
![Page 23: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/23.jpg)
Companding Functions
![Page 24: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/24.jpg)
Method of Companding□ For the compression, two laws are adopted: the -law
in US and Japan and the A-law in Europe.
□ -law□
□ A-law
□ The typical values used in practice are: =255 and A=87.6.
□ After quantization the different quantized levels have to be represented in a form suitable for transmission. This is done via an encoding process.
)1ln(
)1ln(maxmax
VV
out
inVV
11
ln1
)ln(1
10
ln1
max
max
max
out
inVV
out
inVV
out
V
V
AA
AAV
V
A
AV
Vin
in
Vmax= Max uncompressed analog input voltage
Vin= amplitude of the input signal at a particular of instant time
Vout= compressed output amplitude
A, = parameter define the amount of compression
![Page 25: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/25.jpg)
Example 3
□A companding system with µ = 255 used to compand from 0V to 15 V sinusoid signal. Draw the characteristic of the typical system.
□Draw an 8 level non-uniform quantizer characteristic that corresponds to the mentioned µ.
![Page 26: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/26.jpg)
Cont’d...
μ-law A-law
![Page 27: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/27.jpg)
PCM Line Speed
□ The data rate at which serial PCM bits are clocked out of the PCM encoder onto the transmission line.
□ Where□Line speed = the transmission rate in bits per
second□Sample/second = sample rate, fs
□Bits/sample = no of bits in the compressed PCM code
sample
bitsX
second
samples speed line
![Page 28: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/28.jpg)
Example 4
□For a single PCM system with a sample rate fs = 6000 samples per second and a 7 bits compressed PCM code, calculate the line speed.
![Page 29: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/29.jpg)
Virtues & Limitation of PCM
The most important advantages of PCM are:□Robustness to channel noise and
interference.□Efficient regeneration of the coded
signal along the channel path.□Efficient exchange between BT and SNR.
□Uniform format for different kind of base-band signals.
□Flexible TDM.
![Page 30: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/30.jpg)
Cont’d…□Secure communication through the use of
special modulation schemes of encryption.□These advantages are obtained at the cost of
more complexity and increased BT.
□With cost-effective implementations, the cost issue no longer a problem of concern.
□With the availability of wide-band communication channels and the use of sophisticated data compression techniques, the large bandwidth is not a serious problem.
![Page 31: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/31.jpg)
Time-Division Multiplexing
□This technique combines time-domain samples from different message signals (sampled at the same rate) and transmits them together across the same channel.
□The multiplexing is performed using a commutator (switch). At the receiver a decommutator (switch) is used in synchronism with the commutator to demultiplex the data.
![Page 32: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/32.jpg)
Cont’d…
□ TDM system is very sensitive to symbol dispersion, that is, to variation of amplitude with frequency or lack of proportionality of phase with frequency. This problem may be solved through equalization of both magnitude and phase.
□ One of the methods used to synchronize the operations of multiplexing and demultiplexing is to organize the multiplexed stream of data as frames with a special pattern. The pattern is known to the receiver and can be detected very easily.
![Page 33: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/33.jpg)
Block diagram of TDM-PCM communication system
![Page 34: 4.2 Digital Transmission Outlines □ Pulse Modulation (Part 2.1) □ Pulse Code Modulation (Part 2.2) □ Delta Modulation (Part 2.3) □ Line Codes (Part 2.4)](https://reader031.fdocuments.us/reader031/viewer/2022013112/56649ceb5503460f949b757c/html5/thumbnails/34.jpg)
END OF PART 2.2