ECE 4710: Lecture #8 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) 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 10-20 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 1) No channel noise

2) No system noise

3) Sampling at fs 2 B

Quantization error cannot be fixed

ECE 4710: Lecture #8 7

Quantization

3-bit quantizer = 23 = 8 levels Step size = 16 V / 8 Levels = 2 V / Level Max Roundoff Error = 0.5 (2 V) = 1 V

Continuous

Discrete

ECE 4710: Lecture #8 8

Quantization Error

ECE 4710: Lecture #8 9

Encoding

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

Note that discrete voltage amplitude does not equal binary value 111 7 V!!

Digital Word = Code Word

Gray Coding

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 words @ 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 aliasingPre-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

sPCM fnRB2

1

2

1

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

sPCM fnRB2

1

2

1min

f

PSD

1 / Tb = FNBW

000 0 01 1 1

Bit Period = Tb

Signal BW = Bs 1 / Tb

+V

0

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

sPCM fnRB

sPCM fnRB2

1

2

1min

BnfnRB sPCM 2

1

2

1min

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 !!!

BnfnRB sPCM 2 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)