1. Formatting and Baseband Modulation
Chapter Two
Formatting and Baseband Modulation

2. Digital Communication Transformation

3. Formatting and Transmission of Baseband Signals

4. Message, Characters, and Symbols

5. 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

6. Impulse Sampling (Ideal Case)

7. Spectra for Various Sampling Rate
Sampled spectrum (fs > 2fm)
Sampled spectrum (fs < 2fm)

8. Natural Sampling

9. Comparison of Impulse Sampling and Natural Sampling
Impulse sampling (Ideal case)
Natural sampling (A practical way)

10. 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

11. Aliasing for Sampling

12. Eliminate Aliasing for Higher Sampling

13. Aliasing Elimination Higher sampling rate
Pre-filtering the original spectrum so that the new maximum frequency is 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 information
Trade-off is required between the sampling rate and cutoff bandwidth
Engineer’s version of the Nyquist sampling rate is

14. Pre-filter Eliminates Alias

15. Post-filter Eliminates Alias

16. Alias Frequency by Sub-Nyquist Sampling Rate

17. Sampling Process (I)
Without oversampling (sampling rate is the Nyquist rate)
The analog signal passes through a high performance analog low-pass 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 processed by the following digital signal process

18. Sampling Process (II)
With over-sampling (sampling rate is higher than the Nyquist 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 band-limited signal
The samples are mapped to a finite list of discrete output levels and processed by a high performance digital filter to reduce the bandwidth of the digital samples

19. Analog Source Description

20. Source of Corruption Sampling and quantizing effects Channel 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)

21. Quantization Level

22. Signal to Noise Ratio for Quantized Pulse
Assume the quantization error ,e, is uniformly distributed over a single interval q-wide, the quantizer error variance is
The peak power is
The ratio of signal peak power to average quantization error power

23. Quantization Samples

24. 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)

25. Statistics of Speech Amplitudes

26. Uniform and Non-uniform Quantization

27. Quantizer Characteristics

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

29. Compression Functions
m-law compression
A-law

30. Baseband Transmission

31. Waveform Representation of Binary Digits
Binary digits needs to be represented by physical waveform

33. 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

34. Spectral Densities of Various PCM Waveform

35. 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

36. 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
What is the minimum number of bits/sample, or bits/PCM word that should be used in digitizing the analog waveform?
What is the minimum required sampling rate, and what is the resulting bit transmission rate?
What is the PAM pulse or symbol transmission rate?
If the transmission bandwidth equals 12 KHz, determine the bandwidth efficiency for this system

37. Correlative Coding
Transmit 2W symbols/s with zero ISI, using the theoretical minimum bandwidth 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

38. Duobinary Decoding Example
Binary digit sequence xk:
Bipolar amplitudes xk :
Coding rule yk=xk+xk
Decoding decision rule
If , decide that
If , decide opposite of the previous decision
Error propagation could cause further errors

39. Precoded Doubinary Signaling

40. Duobinary Precoding Example Binary digit sequence 0 0 1 0 1 1 0
Precoded sequence
Bipolar sequence
Coding rule
Decoding decision rule
If , decide that
If , decide that
Decoded binary sequence

41. Duobinary Equivalent Transfer Function

42. Duobinary Transfer Function

43. Comparison of Binary with Duobinary Signaling
Binary signaling assumes the transmitted pulse amplitude are independent of one another
Duobinary signaling introduces correlation between pulse amplitudes
Duobinary technique achieve zero ISI signal transmission using a smaller system bandwidth
Duobinary coding requires three levels, compared with the usual two levels for binary coding
Duobinary signaling requires more power than binary signaling (~2.5 dB greater SNR than binary signaling)