dept. of ee, ndhu 1 chapter two formatting and baseband modulation

1Dept. of EE, NDHU

Chapter Two

Formatting and Baseband Modulation

2Dept. of EE, NDHU

Digital Communication Transformation

3Dept. of EE, NDHU

Formatting and Transmission of Baseband Signals

4Dept. of EE, NDHU

Message, Characters, and Symbols

5Dept. of EE, NDHU

Formatting Analog Information

• Formatting process

– Transform an analog waveform into a form that is compatible with a

digital communication system

• Sampling theorem

– A bandlimited signal having no spectral components above hertz

can be determined uniquely by values sampled at

, where is also called the

Nyquist rate

(2.1) sec 2

1

ms fT mf2

mf

6Dept. of EE, NDHU

Impulse Sampling (Ideal Case)

7Dept. of EE, NDHU

Spectra for Various Sampling Rate

Sampled spectrum (fs > 2fm)

Sampled spectrum (fs < 2fm)

8Dept. of EE, NDHU

Natural Sampling

)/(csin)/1( , ssn TnTTC

n

nsnp nffCfX )()(

9Dept. of EE, NDHU

Comparison of Impulse Sampling and Natural Sampling

• Impulse sampling (Ideal case)

• Natural sampling (A practical way)

n

ns

ss nffX

TX )(

11

sn

n

nss

s

n

nsns

TC

TnffXTnTcT

nffXCX

1

0 when ,)()/(sin1

)(1

10Dept. of EE, NDHU

Sample-and-Hold Operation

• Transfer function

where is the hold-operation and is the form of

• Two effects of hold-operation

– The significant attenuation of the higher frequency components

– The non-uniform spectral gain

• Post-filtering operation can compensate the effects of hold-

operation

(2.16) 1

)()(

ns

ss )X(f-nf

TfpfX

)( fp ss cfTT sin

)( fp

11Dept. of EE, NDHU

Aliasing for Sampling

12Dept. of EE, NDHU

Eliminate Aliasing for Higher Sampling

13Dept. of EE, NDHU

Aliasing Elimination

• Higher sampling rate

• Pre-filtering the original spectrum so that the new maximum frequency i

s reduced to fs/2 or less

• Post-filtering removes the aliased components

• Both the pre-filtering and the post-filtering will result a loss of signal inf

ormation

• Trade-off is required between the sampling rate and cutoff bandwidth

• Engineer’s version of the Nyquist sampling rate is ms ff 2.2

14Dept. of EE, NDHU

Pre-filter Eliminates Alias

15Dept. of EE, NDHU

Post-filter Eliminates Alias

16Dept. of EE, NDHU

Alias Frequency by Sub-Nyquist Sampling Rate

17Dept. of EE, NDHU

Sampling Process (I)

• Without oversampling (sampling rate is the Nyquist rate)

– The analog signal passes through a high performance analog low-pas

s filter

– Sampling rate is the Nyquist rate for the band-limited signal

– The samples are mapped to a finite list of discrete output levels and p

rocessed by the following digital signal process

18Dept. of EE, NDHU

Sampling Process (II)

• With over-sampling (sampling rate is higher than the Nyquis

t rate)

– The analog signal passes through a low performance analog low-pass

filter

– The pre-filtered signal is sampled at the higher Nyquist rate for the b

and-limited signal

– The samples are mapped to a finite list of discrete output levels and p

rocessed by a high performance digital filter to reduce the bandwidth

of the digital samples

19Dept. of EE, NDHU

Analog Source Description

20Dept. of EE, NDHU

Source of Corruption

• Sampling and quantizing effects

– Quantization noise due to round-off or truncation error

+ Increase the number of levels employed in the quantization process

– Quantizer saturation

+ AGC can be used to avoid the saturation

– Timing jitter

+ Stable clock

• Channel effects

– Channel noise (thermal noise, interference from other users)

– Intersymbol interference (ISI)

21Dept. of EE, NDHU

Quantization Level

22Dept. of EE, NDHU

Signal to Noise Ratio for Quantized Pulse

• Assume the quantization error ,e, is uniformly distributed over a single i

nterval q-wide, the quantizer error variance is

• The peak power is

• The ratio of signal peak power to average quantization error power

12

1)(

2

2/

2/

2/

2/

222

q

deq

edeepeq

q

q

q

222 )2

(]2

)1([

LqLqVp

22

22

312/

4/)( L

q

qL

N

Sq

23Dept. of EE, NDHU

Quantization Samples

24Dept. of EE, NDHU

Pulse Code Modulation (PCM)

• Quantize PAM signal into a digital word

• Increase the number of levels

– Reduce the quantization noise

– Increase the number of bits per PCM sequence

– The data rate is thus increased, and the cost is a greater transmission

bandwidth

• Some communication systems can be tolerable to the time delay so that

the more quantization levels need not more bandwidth (ex: outer space

communication)

25Dept. of EE, NDHU

Statistics of Speech Amplitudes

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Uniform and Non-uniform Quantization

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Quantizer Characteristics

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Compression Characteristics

Figure 2.20 Compression characteristics. (a) μ-law characteristic. (b) A-law characteristic.

29Dept. of EE, NDHU

Compression Functions

• -law compression

• A-law

xxx

yy sgn)1log(

)]/(1log[ maxmax

11

sgnlog1

)]/(log[1

10 sgn

log1

)/(

max

maxmax

max

maxmax

x

x

Ax

A

xxAy

Ax

xx

A

xxAy

y

30Dept. of EE, NDHU

Baseband Transmission

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Waveform Representation of Binary Digits

• Binary digits needs to be represented by physical waveform

32Dept. of EE, NDHU

33Dept. of EE, NDHU

PCM Waveform Considerations

• DC component

– Eliminate DC energy to enable the system to be ac coupled

• Self-clocking

– Some PCM coding schemes aid in the recovery of the clock signal

• Error detection

• Bandwidth compression

– Such as multi-level codes

• Differential encoding

• Noise immunity

– Some PCM schemes have better error performance

34Dept. of EE, NDHU

Spectral Densities of Various PCM Waveform

35Dept. of EE, NDHU

Bits per PCM Word and Bits per Symbol

• PCM word size

– Required number of bits per analog sample for the allowable

quantization distortion

– For example, we specified the quantization error is specified not to

exceed a fraction of the peak-to-peak analog voltage ,

• Bits per symbol is decided by M-level signal transmission

p ppV

e

pppppppp pVL

V

L

V

L

Ve

2

2)1(2max

bits 2

1log levles

2

12 2 p

lp

Ll

36Dept. of EE, NDHU

Quantization Levels and Multi-level Signaling

• Example 2.3

– The information in an analog waveform, with the maximum frequency fm=3 kHz, is to

be transmitted over an M-ary PAM system, where the number of pulse levels is M=16.

The quantization distortion is specified not to exceed of the peak-to-peak analog

signal

(a) What is the minimum number of bits/sample, or bits/PCM word that should be used i

n digitizing the analog waveform?

(b) What is the minimum required sampling rate, and what is the resulting bit transmissio

n rate?

(c) What is the PAM pulse or symbol transmission rate?

(d) If the transmission bandwidth equals 12 KHz, determine the bandwidth efficiency for

this system

%1

37Dept. of EE, NDHU

Correlative Coding

• Transmit 2W symbols/s with zero ISI, using the theoretical minimum ba

ndwidth of W Hz, without infinitely sharp filters.

• Correlative coding (or duobinary signaling or partial response signaling)

introduces some controlled amount of ISI into the data stream rather than

trying to eliminate ISI completely

• Doubinary signaling

38Dept. of EE, NDHU

Duobinary Decoding

• Example

– Binary digit sequence xk: 0 0 1 0 1 1 0

– Bipolar amplitudes xk : -1 -1 +1 -1 +1 +1 -1

– Coding rule yk=xk+xk-1 -2 0 0 0 2 0

– Decoding decision rule

+ If , decide that

+ If , decide that

+ If , decide opposite of the previous decision

• Error propagation could cause further errors

1ˆ kx

0ˆ kx

2ˆ ky

2ˆ ky

0ˆ ky

39Dept. of EE, NDHU

Precoded Doubinary Signaling

40Dept. of EE, NDHU

Duobinary Precoding

• Example

– Binary digit sequence 0 0 1 0 1 1 0

– Precoded sequence 0 0 1 1 0 1 1

– Bipolar sequence -1 -1 +1 +1 -1 +1 +1

– Coding rule -2 0 +2 0 0 +2

– Decoding decision rule

+ If , decide that

+ If , decide that

+ Decoded binary sequence 0 1 0 1 1 0

1 kkk wxw

}{ kx

}{ kw

1 kkk wwy

2ˆ ky

0ˆ ky

0ˆ kx

1ˆ kx

}ˆ{ kx

41Dept. of EE, NDHU

Duobinary Equivalent Transfer Function

fTjefH 21 1)(

elsewhere 02

1for cos2)(

that so

)(

)1(

2

1for )()()(

2

21

TfTfH

eeeT

Te

TffHfHfH

e

fTjfTjfTj

fTj

e

elsewhere 02

1for )(2 T

fTfH

)(sin)(sin)( T

Ttc

T

tcthe

42Dept. of EE, NDHU

Duobinary Transfer Function

43Dept. of EE, NDHU

Comparison of Binary with Duobinary Signaling

• Binary signaling assumes the transmitted pulse amplitude are independe

nt of one another

• Duobinary signaling introduces correlation between pulse amplitudes

• Duobinary technique achieve zero ISI signal transmission using a smalle

r system bandwidth

• Duobinary coding requires three levels, compared with the usual two lev

els for binary coding

• Duobinary signaling requires more power than binary signaling (~2.5 dB

greater SNR than binary signaling)