COMMUNICATION SYSTEM EEEB453Chapter 5 (Part III)

DIGITAL TRANSMISSION

Intan Shafinaz MustafaDept of Electrical Engineering

Universiti Tenaga Nasionalhttp://metalab.uniten.edu.my/~shafinaz

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Signal to Quantization Noise Ratio (SQR) Linear codes – the magnitude change between any two successive

codes is the same i.e the quantum/quantization interval is equal, thus the magnitude of the quantization errors are also equal.

Recall, maximum quantization noise, Qe = ½ quantum = Vlsb/2, Then worst-case (minimum) voltage SQR (occurs when input signal

is at its minimum amplitude) is

Maximum SQR occurs at the maximum signal amplitude, i.e From previous example,

22min

lsb

lsb

e VV

QresolutionSQR

dBSQR dB 62log20min,

65.03max

max eQ

VSQR

dBSQR dB 6.156log20max,

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Signal to Quantization Noise Ratio (SQR) From the example, even though the magnitude of the Qe remains constant, the

percentage of error decreases as the magnitude of the sample increase.Thus, SQR is not constant.

For linear PCM code i.e all quantization intervals have equal magnitude, SQR or SNR is defined as

Generally,SQRdB = 10.8 + 20 log v/q

where v = rms signal voltageq = quantization interval

or SQRdB = 6.02n + 1.76 where n = no. of bits

powernoiseonquantizatiavgpowersignalavgSQRdB log10

RqRvSQRdB /12

log10 2

2 12log10 2

2

qv (assume equal R)

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Example 5 – A digitizing system specifies 55 dB of dynamic range. How many bits are required to satisfy the dynamic range specification? What is the signal-to-noise ratio for the system?

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Uniform and Non-uniform Quantization

In uniform (linear) quantization – each quantum interval is the same step size

In nonuniform (non-linear) coding – each quantum interval step size may vary in magnitude

How can the quantization error be modified in a nonuniform PCM system so that an improve SNR result?

Notice that poor resolution is present in the weak signal regions, yet the strong signal exhibit a reasonable exact copy of the original signal.

Figure also shows how the quantum interval can be changed to provide smaller step-sizes within the area of the weak signal.This will result in an improved SNR for the weak signal.

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SQR at lower amplitude < SQR at higher amplitude

Lower amplitude values are relatively more distorted

More of voice signal is at lower amplitude

Reduce step size at lower amplitude

More accuracy at lower amplitude

Sacrifices SQR at higher amplitude

Provides higher dynamic range

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Linear versus Nonlinear PCM Codes. For linear coding, accuracy of the higher amplitude analog signal is the

same as for the lower amplitude signal. SQR for lower amplitude signal is less than the higher amplitude signal. For voice transmission, low amplitude signals are more likely to occur

than large amplitude signals. Thus a nonlinear encoding is the solution. With non-linear coding, the step size increases with the amplitude of the

input signal. Nonlinear encoding gives larger dynamic range. SQR is sacrificed for higher amplitude signals to achieve more accuracy

for the lower amplitude signals. However, it is difficult to fabricate nonlinear ADC.

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Companding Companding is the process of compressing and then expanding. Higher amplitude analog signals are compressed (amplified less)

prior to Tx and then expanded (amplified more) at the Rx. It improves the dynamic range.

Notice, how the weak portion of the input is made nearly equal to the strong portion by the compressor but restored to the proper level by the expander.Companding is essential to quality transmission using PCM.

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Input signal with DR of 50dB is

compressed to 25dB at Tx

Expanded back to its original DR of 50dB at Rx

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The input-output characteristics of a compressor are shown in Fig. (b). The horizontal axis is the normalized input signal i.e

The compressor maps input signal increment, m into larger increments y for small input signals, and vice versa for large input signal.

inputnormalizedVV

mm in

p

max

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Analog Companding In the transmitter, the DR of the analog signal is compressed,

sampled and then converted to a linear PCM code. In the receiver, the PCM code is converted to a PAM signal,

filtered, and then expanded back to its original DR

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2 methods of analog companding :i. μ-Law - use in Japan and US

Vmax= maximum uncompressed analong input amplitude (V) Vin = amplitude of the input signal at a particular instant of time (V) μ = parameter to define the amount of compression (unitless) =

255Vout = compressed output amplitude (V)

ii. A-law – use in Europe

Analog Companding

)1ln()1ln( max

VVVV inp

out

AVV

AVVA

VV ininout

10ln1 max

maxmax

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ln1ln1

max

max

VV

AAVVA inin

For voice Tx which requires minimum DR of 40dB, μ=255 and A=87.6 gives comparable result and has been standardize by CCITT.

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μ-Law Characteristic A-Law Characteristic

The μ parameter defines the amount of compression (i.e the range of signal power in which the SQR is relatively constant.

Note μ = 0 indicates no compression and the voltage gain curve is linear. Higher value of μ yield nonlinear curves.

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Example 6 - For a compressor with a μ = 255, determine a. The voltage gain for the following relative values of Vin : (i) Vmax (ii) 0.75Vmax (iii) 0.5Vmax (iv) 0.25Vmax

b. The compressed output voltage for a maximum input voltage of 4V

c. Input and output DR and compression.