4.2 digital transmission outlines □ pulse modulation (part 2.1) □ pulse code modulation (part...
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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)
□Basic scheme of PCM system□Quantization□Quantization Error□Companding□Block diagram & function of TDM-PCM
communication system
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.
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.
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)
4 Steps Process
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.
PCM Example
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).
Cont’d...
Analog input signal
Sample pulse
PAM signal
PCM code
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…
□ A difference between the exact value of the analog signal & the nearest quantization level.
QUANTIZATION ERROR
Types of Quantization
Midtread Midrise
Types of Quantizer1. Uniform type : The levels of the quantized amplitude are uniformly spaced. 2. Non-uniform type : The levels are not uniform.
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
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
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
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
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.
Effect of Non-Linear Coding
Nonlinear Encoding
□ Quantization levels not evenly spaced
□ Reduces overall signal distortion
□ Can also be done by companding
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.
Companding Functions
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
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.
Cont’d...
μ-law A-law
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
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.
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.
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.
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.
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.
Block diagram of TDM-PCM communication system
END OF PART 2.2