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II.A Baseband Transmission

Pulse Amplitude Modulation (PAM)

Natural sampled PAMInstantaneous sampled PAM

Time division multiplexing (TDM)

Intersymbol interference (ISI)

Pulse Width Modulation (PWM)

Pulse Position Modulation (PPM)Pulse Code Modulation (PCM)

Definition

Quantization noise issues

Signal-to-Quantization Noise ratio (SNRq)

Nonlinear quantization

Pre-emphasis & de-emphasisApplication to speech signal type

m-law & A-law quantization for speech types

TDM for digital signals

Delta modulation

Adaptive Delta modulation

Receivers

PAM, PPM, PWM receivers

Digital Baseband

Signal format & power spectrum concepts

Potential problems with NRZ transmissions

(Definitions & Modulation types)

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II. Baseband Transmission

Goal: Investigate information transmissionusing 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)

ffm fm

S1(f)

f

Sm(f)

f

Natural Sampled PAM from the frequency side

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S(f)

ffm 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)

ffm fm

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s(t) sm(t)

sc(t)

( )sin t

s t t

p

p

=

sc(t)

tt t T

Compute the Fourier transform forsm(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 multiple

poles 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 )( ) m

f ts t

t

p

p

=

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 2

2 1 8 /

f t KTfh t A

f t K f t

p p

p p

=

-

Krepresents 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 effectiveness

of a quantization scheme

- Quantization noise level is directly related to the

number of quantization levels

- Assume quantization errore(n) to be equally likelyto occur in the range D

pdf ofe

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 2

sq

e

E s nSNRE e n

s

s

= =

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Example

( ) ( )2cos 500t tp=

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 applyingBefore applyingmumu-law-law After applyingAfter applyingmumu-law-law

Comments ?

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Mu-Law / A-Law quantization for voicetransmission

Mu-Law (USA-Japan); m = 255

Mu-Law (Europe-South America); A = 87.56

( ) ( ) ( )( )

1sgn

1

In sF s s

In

m

m

+

=

+

( ) ( ) ( )

( )( )( )

1sgn ; 01

1 1sgn ; 1

1

A sF s s sIn A A

In A ss s

In A A

= =0, 0 for x

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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

m-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 issuesslope overload granular noise

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Adaptive delta modulation

designed to overcome slope overload andgranular noise issues

Song algorithm: compares transmitted bitwith previous bit.

If same

If different

; 1

; 1

K K

K K

D = D >

D = D same contribution is added in each period

=> restrict integration over one period only

2/ 2

2

/ 2

22

1( )

sin( )

b

b

Tj ft

Tb

b

b

b

G f Ve dt T

fTV T

fT

p

p

p

-

-

=

=

2/ 2

2

/ 2

1

( ) lim ( )

Tj ft

TTG f s t e dt T

pD

-

- DD

= D

Def: The PSD for a non periodic signal s(t) is

defined as:

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Def: Nominal signal bandwidth: Signal bandwidth up to

the 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 by

the actual signal level