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II.A Baseband Transmission

Pulse Amplitude Modulation (PAM)Natural sampled PAMInstantaneous sampled PAMTime division multiplexing (TDM)Intersymbol interference (ISI)

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

Delta modulationAdaptive Delta modulationReceivers

PAM, PPM, PWM receiversDigital BasebandSignal format & power spectrum conceptsPotential problems with NRZ transmissions

(Definitions & Modulation types)

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II. Baseband Transmission

• Goal: Investigate information transmission using low frequencies

1) Pulse Amplitude Modulation (PAM)• Natural-sampled PAM

�s(t)sm(t)

sc(t)

s(t)

t

sc(t)

t

sm(t)

t

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S(f)

f– fm fm

S1(f)

f

Sm(f)

f

• Natural Sampled PAM from the frequency side

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S(f)

f– fm fm

H(f)

S1(f)

f

f

• Natural Sampled PAM from the frequency side

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�s(t)sm(t)

sc(t)

H(f)s1(t)

• Instantaneous-sampled PAM

s(t)

t

sc(t)

t

s1(t)

t

t

sm(t)

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H(f)

S1(f)

f

f

Sm(f)

f

• 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