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Pulse Width Modulation (PWM)Pulse Position Modulation (PPM)Pulse Code Modulation (PCM)
DefinitionQuantization noise issuesSignal-to-Quantization Noise ratio (SNRq)Nonlinear quantizationPre-emphasis & de-emphasisApplication to speech signal type�-law & A-law quantization for speech typesTDM for digital signals
• Instantaneous Sampled PAM from the frequency side
S(f)
f– fm fm
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�s(t) sm(t)
sc(t)
� �sin ts t
t�
�
�
sc(t)
t– � � T
Compute the Fourier transform for sm(t)
• Example
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2) Time Division Multiplexing (TDM)
Multiplexing of 2 channels
Multiplexing of 10 channels
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Figure 2.14 - Sub- and Super-CommutationFigure 2.14 - Sub- and Super-Commutation
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• What is it ?
Interaction between multiplepoles due to transmissionchannel distortions.
3) Intersymbol Interference (ISI)
• Overlap of signals into adjacent time slots
Pulse through LPF
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Pulse shaping by the Channel
sin(2 )( ) mf t
s tt�
�
�
1/ 2 mf
2fm
Ideal LPF Shaping
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•How is ISI evaluated ?
=>Through eye pattern generation.
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==> Raised cosine filter
� �� � � �
� �0 0
2 20 0
sin 2 cos 22 1 8 /
f t KTfh t A
f t K f t� �
� �
�
�
K represents flat portion width of the frequency transform
Raised Cosine Impulse Response
• How to fix the problem ?
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Raised Cosine Frequency Characteristic
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s(t) sm(t)
sc(t)
PWM
4) Pulse Width Modulation (PWM)
PWM
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• PWM Generator
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5) Pulse Position Modulation (PPM)
• PPM can be derived from PWM
PWM to PPM
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• Signal format
6) Pulse Code Modulation (PCM)
• From analog to digital
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• Quantization noise issues
- Quantization error is a measure of effectivenessof a quantization scheme
- Quantization noise level is directly related to thenumber of quantization levels
- Assume quantization error e(n) to be equally likelyto occur in the range D
pdf of e
p(e)
e
s(t)
t
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• e(n) statistics
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• SNR level due to quantization noise
� �
� �
22
2 2s
qe
E s nSNR
E e n�
�
� �� �� �� �� �
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• Example
� � � �2cos 500s t t��
1) Compute SNRq when using 8-bit PCM
2) Compute the minimum number of bits needed to get SNRq � 20 dB
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• Non-linear quantization
(pre-emphasis and de-emphasis concepts)
� Goal: to improve quality of signal to be quantized
� Example
S(f)
f60 Hz
signal distortion
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� Example: speech signal
Before applying Before applying mumu-law-law After applying After applying mumu-law-law
Comments ?
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• Mu-Law / A-Law quantization for voice transmission
• Mu-Law (USA-Japan); � = 255
• Mu-Law (Europe-South America); A = 87.56
� � � �� �� �
1sgn
1In s
F s sIn
�
�
�
�
�
� � � �� �
� �� �� �
1sgn ; 01
1 1sgn ; 11
A sF s s s
In A A
In A ss s
In A A
� � �
�
�
� �
�
s(n) F(S(n))Companding
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Input-output characteristic for �-law companding
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�-255 Piecewise linear approximation
Same resolution whichwould be obtained fromlinear quantization
1 bit for polarity (1 for x>=0, 0 for x<0)3 bits for identifying the segment4 bits to identify quantization level within each segment
Approximate the �-255 curve by a piecewise linear curveDivide output region into 8 unequal segments (for positive side)Within each segment, uniformly quantize using 4 bits (i.e., 16 regions)
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• TDM for digital signals
Example: TDM in T – 1 system
� designed for short distances (15 to 65 km)
� 1.544 megabits/s pulse signal developed for transmission
� signal developed by 24 channel TDM
� each channel sampled at 8 KHz, with 8-bit �-law companding
� each frame each 24 � 8 bits
192 bits used for information 1 bit used for frame synchronization
� transmission rate is
8000 frames/s � 193 bits/frame =
1.544 Mbits/sec
TDM in T-1
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7) Delta Modulation
• Simplified 1-bit PCM
• Quantization issues
slope overload granular noise
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• Adaptive delta modulation
– designed to overcome slope overload and granular noise issues
– Song algorithm: compares transmitted bit with previous bit.
If sameIf different
; 1; 1
K KK K
�� � � �
�� � � �
Song Algorithm
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8) PAM, PPM & PWM Receivers
• PAM receiver (Instantaneous-Sampled PAM)
• Recall frequency transform for for natural-Sampled PAM
f
S(f)
f
Sm(f)
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• Sample-and-Hold for PAM demodulation
LPFPAM s(t)
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• PWM & PPM receivers
2-step process
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9) Digital Baseband
Unipolar/Bipolar waveforms
• Signal Format
RZ & NRZ waveforms
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• Power Spectrum (Ex: Periodic NRZ)
t
s(t)
Tb Rb=1/TbTb=T/2
a) Power Spectrum of s(t) ( periodic case: 0 1 0 1 0 …)
V
-V
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Figure 2.27
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b) Power Spectrum of random NRZ (Extension to nonperiodic s(t) case)
-Use concept of power spectral density (PSD)
- Assume that �T increases in multiples of the bit length (Tb)=> same contribution is added in each period=> restrict integration over one period only
2/ 2 2
/ 2
22
1( )
sin( )
b
b
T j ft
Tb
bb
b
G f Ve dtT
fTV T
fT
�
�
�
�
�
�
� �� � �
� �
�
2/ 2 2
/ 2
1( ) lim ( )T j ft
TTG f s t e dt
T�
��
��� ��
� �� � ��� �
�
Def: The PSD for a non periodic signal s(t) isdefined as:
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Def: Nominal signal bandwidth: Signal bandwidth up tothe 1st zero of signal spectral lobe
What is the above signal nominal bandwidth ?
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• Potential problems with NRZ transmissions
- No transition between one bit to the next- Potential data inversion problems
- Differential coding option:data is represented as changes in levels rather than bythe actual signal level