1. Pulse Code Modulation
Pulse Code Modulation (PCM) : method for conversion from analog to digital waveform
Instantaneous samples of analog waveform represented by digital code words output in serial bit stream
Digital Code Words
n-bit binary digital word has M = 2n unique codes
Each code word represents a specific discrete amplitude value of analog waveform
Analog signal has infinite # of amplitude levels so discrete PCM amplitude introduces error
Discrete value is closest value to actual amplitude
“Quantizing” or “Roundoff” error
ECE 4710: Lecture #8

2. Pulse Code Modulation Widely used for digital landline telephony
Advantages
Simple and inexpensive digital circuits can be used
Multiple types of data (voice, video, internet, etc.) can be merged (interleaved) together into a single signal and transmitted over same channel
Time Division Multi-plexing  TDM
Clean PCM waveforms can be regenerated at repeater stations over long-distance communication links
Noisy input PCM signal replaced with clean output PCM signal, perhaps with a few bit errors
ECE 4710: Lecture #8

3. Pulse Code Modulation Advantages (continued) Primary Disadvantage
S/N performance of digital signal can be much superior to analog signal
Errors can be detected and corrected using channel codes
Primary Disadvantage
PCM signals typically have times the bandwidth of the input analog signal
Very inefficient use of spectrum
Not used for most wireless applications
ECE 4710: Lecture #8

4. PCM Generation Basic steps for generating PCM signal
Bandlimit input analog signal to prevent aliasing (optional)
Instantaneous sample and hold circuit to convert analog signal to flat-top PAM
Quantize the PAM signal to produce discrete amplitude levels for analog PAM  “Quantized PAM”
Quantize or roundoff error is irrevocably introduced
PCM signal generated by taking discrete amplitude and generating a coded digital word to represent amplitude value
Codes selected to minimize effect of bit errors
ECE 4710: Lecture #8

5. PCM System
PCM Signal
ECE 4710: Lecture #8

6. PCM Quantization
Uniform quantization divides signal amplitudes in to M = 2n equally spaced levels
Approximation of analog amplitude with discrete value
Error will be one-half of quantization step size
Quantization error
Even if
No channel noise
No system noise
Sampling at fs  2 B
 Quantization error cannot be fixed
ECE 4710: Lecture #8

7. Quantization ECE 4710: Lecture #8 3-bit quantizer = 23 = 8 levels
Step size = 16 V / 8 Levels = 2 V / Level
Max Roundoff Error = 0.5 (2 V) = 1 V
Discrete
Continuous
ECE 4710: Lecture #8

8. Quantization Error
ECE 4710: Lecture #8

9. Encoding ECE 4710: Lecture #8
Encoding transforms quantized PAM signal into PCM signal
Each discrete amplitude level represented by unique code word
Codes selected to minimize impact of single bit errors or multiple sequential bit errors on signal quality
Gray Code
One-bit change between code words representing adjacent amplitude values (as much as possible)
Single bit errors (excluding sign bit) have small impact
Reed-Solomon Codes
Correct sequential “burst” errors, e.g. errors that occur in sequential groups
Used on CD’s to minimize impact of scratches or fingerprints
ECE 4710: Lecture #8

10. Gray Coding ECE 4710: Lecture #8
Note that discrete voltage amplitude does not equal binary value  111  7 V!!
Digital Word = Code Word
ECE 4710: Lecture #8

11. Coded PCM Signal
Coded word output in serial bit stream of n-bit digital words
Many types of rectangular pulse shapes used to represent binary 1’s and 0’s
Above example shows unipolar non-return to zero shape
Unipolar NRZ (Fig. 3-15b, pg. 165)
ECE 4710: Lecture #8

12. PCM Circuits PCM circuit combines functions on a single chip
Sample & Hold + Quantizer + Encoder
Analog-to-Digital Conversion = ADC
Digital-to-Analog Conversion = DAC
Decode PCM to produce analog signal
Many chips are specialized for particular application
Voice for telephony, audio for music, video, data, etc.
Combination of Coder / Decoder = “Codec”
Similar to Modulate / Demodulate = Modem
ECE 4710: Lecture #8

13. PCM Signal BW
Spectral shape of PCM signal is completely unrelated to spectral shape of input analog signal
Spectral shape depends on type of digital pulse waveform used to represent serial PCM data
PCM signal BW is indirectly related to input analog signal BW but it also depends on other factors
Number of bits
Sampling rate
BW of serial pulse representing code words
ECE 4710: Lecture #8

14. PCM Signal BW Bit rate of binary data  R = n fs (bits per sec = bps)
e.g. 8-bit code 5000 samples/sec = 40 kbps
For no aliasing we require fs  2 B where B is the bandwidth of the input analog signal
What kind of bandwidth measure is B?
Absolute bandwidth for no aliasing
Pre-filter usually done to obtain absolutely bandlimited input
PCM signal bandwidth is bounded by
Minimum BW only obtained for (sin x) / x pulse shape
Not practical for most systems
ECE 4710: Lecture #8

15. PCM Signal BW Rectangular-like pulse is usually used for PCM waveforms
PCM signal BW will be larger than minimum:
How much larger?
Depends on type of line signals (RZ, NRZ) and pulse shapes (studied next)
Typical BW for common line codes and pulse shapes
Unipolar NRZ, Bipolar NRZ, Bipolar RZ  First-Null BW = R = 1 / Tb f
PSD
1 / Tb = FNBW 1
Bit Period = Tb
Signal BW = Bs  1 / Tb +V
ECE 4710: Lecture #8

16. PCM Signal BW
Typical rectangular pulses  PCM signal will have FNBW of
Minimum BW was
For Nyquist rate sampling fs = 2 B so minimum BW
ECE 4710: Lecture #8

17. PCM Signal BW Typical FNBW
For reasonable values of n, PCM signal BW will many times larger than input analog signal BW
Primary disadvantage of PCM
Example: Landline digital telephony
Voice signal BW  300 Hz to 3,300 Hz
fs  2 B = 2 • 3300 = 6.6 kHz but chosen to be fs = 8 kHz to allow inexpensive (non-ideal) LPF
n = 8-bit code word  M = 256 level quantizer
BPCM = n fs = 8 • 8000 = 64 kHz FNBW
~ 20  larger than 3.3 kHz input analog signal !!!
Only for Nyquist rate sampling
ECE 4710: Lecture #8

18. PCM Signal Filtering
Filtering (LPF) of PCM rectangular pulse can be done to reduce signal BW by ~20-40%
FNBW still many times larger than analog signal BW
LPF will cause time smearing of rectangular pulses
Care must be taken so that pulse smearing from LPF does not create too much ISI  BER 
Even if no LPF is used to reduce PCM signal BW the frequency response of the transmission channel can also cause pulse smearing, ISI, and BER increase
Mobile Radio Channel (wireless cellular)
ECE 4710: Lecture #8