Topics for the Session

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Topics for the Session

• Non- uniform Quantizers.
• DPCM

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UNIFORM - QUANTIZER

• Variance,
• Features
• Variance is valid only if the input signal does
  not overload Quantizer
• SNR Decreases with a decrease in the input power
  level.

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ROBUST QUANTIZER
A Quantizer whose SNR remains essentially
constant for a wide range of input power levels.
. Non Uniform Quantizer
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Non Uniform Quantizer

• Variable Step-Size.
• Smaller amplitude - Smaller Step Size.
• Larger amplitude - Large Step size

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Non- UniformQuantizer MODEL
Compander Compressor Expander
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Compressor
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Expander
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Quantization Error-1
Transfer Characteristics
Compressor --- C(x) Expander --- C-1(x)
C(x). C-1(x) 1
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Quantization error-2
Compressor Characteristics ( for large L )

?k Width in the interval Ik
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Quantization Error-3

• Let fX(x) PDF of X .
• Assumptions
• fX(x) is Symmetric
• fX(x) is approximately constant in each
  interval. ie.. fX(x) fX(yk)

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Quantization Error-4
fX(x) fX(yk) ?k xk1 - xk for k 0, 1,
L-1. pk Probability of variable X pk P
(xk lt X lt xk1 ) fX(x) ?k fX(yk) ?k
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Quantization Error-5
Q yk X for xk lt X lt xk1 Variance
sQ2 E ( Q2) E ( X yk )2
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Carrying out Integration w.r.t x
( ?k2 / 12 ) - Variance of error in the
Interval Ik
?k ? for all k in Uniform Quantizer.
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Types of Companding

• µ - law ( US, Canada Japan)
• A - law ( Europe)

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µ-law
?255 reduces noise power in speech 20dB
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µ-law companding
µ 255 - practical value
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A-law
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A-law
Practical value for A 87.5
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Companding Gain - Gc
Companding gain For µ-law
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Advantages ofNon Uniform Quantizer

• Reduced Quantization noise
• High average SNR

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DPCM - Transmitter


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DPCM - Receiver