1. Chapter 2: Formatting and Baseband Modulation

2. Contents Formatting Sampling Theorem Pulse Code Modulation (PCM)
Quantization
Baseband Modulation

3. Introduction

4. Introduction Formatting Baseband Signaling: Pulse modulation
To insure that the message is compatible with digital signal
Sampling : Continuous time signal x(t)  Discrete time pulse signal x[n]
Quantization : Continuous amplitude  Discrete amplitude
Pulse coding : Map the quantized signal to binary digits
When data compression is employed in addition to formatting, the process is termed as a source coding.
Baseband Signaling: Pulse modulation
Convert binary digits to pulse waveforms
These waveforms can be transmitted over cable.

5. Baseband Systems

6. Formatting Textual Data

7. Formatting Textual Data (Cont.)
A system using a symbol set with a size of M is referred to as an M-ary system.
For k=1, the system is termed binary.
For k=2, the system is termed quaternary or 4-ary. M=2k
The value of k or M represents an important initial choice in the design of any digital communication system.

8. Formatting Analog Information
Baseband analog signal
Continuous waveform of which the spectrum extends from dc to some finite value (e.g. few MHz)
Analog waveform  Sampled version
PAM  Analog waveform FT
Sampling process ((e.g.) sample-and-hold)
Low pass filtering

9. Sampling Theorem Uniform sampling theorem
A bandlimited signal having no spectral components above fm hertz can be determined uniquely by values sampled at uniform intervals of

10. Nyquist Criterion
A theoretically sufficient condition to allow an analog signal to be reconstructed completely from a set of uniformly spaced discrete-time samples
Nyquist rate fm fs
Speech
3.2kHz
(사람의 한계)
8 kHz
(휴대폰)
Audio
20kHz
(가청주파수)
44.1kHz (mp3)
e.g.) speech 8kHz
audio kHz

11. Impulse Sampling
In the time domain,
In the frequency domain,

12. Impulse Sampling (Cont.)FT FT FT

13. Impulse Sampling (Cont.)
The analog waveform can theoretically be completely recovered from the samples by the use of filtering (see next figure).
Aliasing
If , some information will be lost.
Cf) Practical consideration
Perfectly bandlimited signals do not occur in nature.
A bandwidth can be determined beyond which the spectral components are attenuated to a level that is considered negligible.

14. Impulse Sampling (Cont.)

15. Aliasing
Due to undersampling
Appear in the frequency band between

16. Sampling and aliasing Helicopter 100Hz Sampling at 220Hz  100Hz f
How about sampling at 120Hz?
-100
100 f
-320
-100
120
340
-340
-120
100
320
540 f
-180
-100
-20 60
-140
-60 20
100 f

17. Aliasing (Cont.)
Effect in the time domain

18. Natural Sampling More practical method
A replication of X(f), periodically repeated in frequency every fs Hz.
Weighted by the Fourier series coefficients of the pulse train, compared with a constant value in the impulse-sampled case.

19. Natural Sampling (Cont.)

20. Sample-and-Hold The simplest and most popular sampling method
Significant attenuation of the higher-frequency spectral replicates
The effect of the nonuniform spectral gain P(f) applied to the desired baseband spectrum can be reduced by postfiltering operation.

21. Oversampling the most economic solution
Analog processing is much more costly than digital one.

22. Quantization Analog  quantized pulse with “Quantization noise”
L-level uniform quantizer for a signal with a peak-to-peak range of Vpp= Vp-(-Vp) =2Vp
The quantization step
The sample value on is approximate to
The quantization error is o

23. Quantization Errors

24. Quantization Errors (Cont’d)
SNR due to quantization errors

25. Pulse Code Modulation (PCM)
Each quantization level is expressed as a codeword
L-level quantizer consists of L codewords
A codeword of L-level quantizer is represented by l-bit binary digits.
PCM
Encoding of each quantized sample into a digital word

26. Pulse Code Modulation (PCM)

27. PCM Word Size How many bits shall we assign to each analog sample?
The choice of the number of levels, or bits per sample, depends on how much quantization distortion we are willing to tolerate with the PCM format.
The quantization distortion error p = 1/(2 # of levels)

28. Uniform Quantization The steps are uniform in size.
The quantization noise is the same for all signal magnitudes.
SNR is worse for low-level signals than for high-level signals.

29. Uniform Quantization (Cont.)

30. Nonuniform Quantization
For speech signals, many of the quantizing steps are rarely used.
Provide fine quantization to the weak signals and coarse quantization to the strong signals.
Improve the overall SNR by
The more frequent  the more accurate
The less frequent  the less accurate
But, we only have uniform quantizer.
Probability
Volt

31. Nonuniform Quantization (Cont.)
Companding = compress + expand
Achieved by first distorting the original signal with a logarithmic compression characteristic and then using a uniform quantizer.
At the receiver, an inverse compression characteristic, called expansion, is applied so that the overall transmission is not distorted.
Probability
Probability o o
Volt
Volt
x[n]
x[n]’
Compression
Quantization
Expansion

32. Nonuniform Quantization (Cont.)Ξ

33. Baseband Transmission
Digits are just abstractions: a way to describe the message information.
Need something physical that will represent or carry the digits.
Represent the binary digits with electrical pulses in order to transmit them through a (baseband) channel.
Binary pulse modulation: PCM waveforms
Ex) RZ, NRZ, Phase-encoded, Multi-level binary
M-ary pulse modulation : M possible symbols
Ex) PAM, PPM (Pulse position modulation), PDM (pulse duration modulation)

34. PCM Waveform Types Nonreturn-to-zero (NRZ) Return-to-zero (RZ)
NRZ-L, NRZ-M (differential encoding), NRZ-S
Return-to-zero (RZ)
Unipolar-RZ, bipolar-RZ, RZ-AMI
Phase encoded
bi--L (Manchester coding), bi--M, bi--S
Multilevel binary
Many binary waveforms use three levels, instead of two.

35. PCM Waveforms (Fig. 2.22)

36. Choosing a PCM Waveform
DC component
Magnetic recording prefers no dc (Delay, Manchester..)
Self-clocking
Manchester
Error detection
Duobinary (dicode)
Bandwidth compression
Duobinary
Differential encoding
Noise immunity

37. Spectral Densities of PCM Waveforms
Normalized bandwidth
Can be expressed as W/RS [Hz/(symbol/s)] or WT
Describes how efficiently the transmission bandwidth is being utilized
Any waveform type that requires less than 1.0Hz for sending 1 symbol/s is relatively bandwidth efficient.
Bandwidth efficiency
R/W [bits/s/Hz]

38. Spectral Densities of PCM Waveforms
Mean = 0  DC=0
Bandwidth efficiency
R/W [bits/s/Hz]
Transition period↑ W ↓ FT

39. Autocorrelation of Bipolar
Note that where xi
xi+1
xi+2
xi-1
x(t) To
2To xi
xi+1
xi+2
xi-1
x(t+Ʈ) -Ʈ
To-Ʈ
2To-Ʈ A2 A2
Rx(Ʈ) -Ʈ To
To-Ʈ
2To
2To-Ʈ

40. Autocorrelation of Bipolar
Note that where
xi+1 xi
xi+2
xi-1
x(t)
2To To xi
xi+1
xi+2
xi-1
x(t+Ʈ) -Ʈ
To-Ʈ
2To-Ʈ A2 A2 A2
Rx(Ʈ) -Ʈ
To-Ʈ To
2To-Ʈ
2To

41. Autocorrelation and power spectrum density of Bipolar
Gx(f) 1 FT

42. Rectangular function Rect(t)FT

43. M-ary Pulse-Modulation
M=2k-levels : k data bits per symbol
 longer transition period
 narrower W
 more channel
Kinds of M-ary pulse modulation
Pulse-amplitude modulation (PAM)
Pulse-position modulation (PPM)
Pulse-duration modulation (PDM)
M-ary versus Binary
Bandwidth and transmission delay tradeoff
Performance and complexity tradeoff

44. Example. Quantization Levels and Multilevel Signaling
Analog waveform fm=3kHz, 16-ary PAM, quantization distortion  1%
(a) Minimum number of bits/sample?
|e|= 1/2L <  L>50  L=64  6bits/sample
(b) Minimum required sampling rate?
fs > 2*3kHz = 6kHz
(c) Symbol transmission rate? 9103symbols/sec
6*6 kbps = 36kbps  36[kbps]/4[bits/symbol]
(d) If W=12kHz, the bandwidth efficiency?
R/W = 36kbps / 12kHz = 3bps/Hz

45. HW#3
P2.2
P2.8
P2.9
P2.14
P2.18