1. technology and computing

Pulse Code Modulation
Lecture 5
Why a Particular Encoding
Technique

Digital data, digital signal


Equipment less complex and expensive than
digital-to-analog modulation equipment
Analog data, digital signal

Permits use of modern digital transmission and
switching equipment
Why a Particular Encoding
Technique

Digital data, analog signal



Some transmission media will only propagate
analog signals
E.g., optical fiber and unguided media
Analog data, analog signal


Analog data in electrical form can be
transmitted easily and cheaply
Done with voice transmission over voice-grade
lines
Criteria For Signal Encoding

What determines how successful a receiver will be
in interpreting an incoming signal?






Signal-to-noise ratio
Data rate
Bandwidth
An increase in data rate increases bit error rate
An increase in SNR decreases bit error rate
An increase in bandwidth allows an increase in
data rate
Factors Used to Compare
Encoding Schemes

Signal spectrum




Clocking



With lack of high-frequency components, less bandwidth
required
With no dc component, ac coupling via transformer possible
Transfer function of a channel is worse near band edges
Ease of determining beginning and end of each bit positionSignal
interference and noise immunity
Performance in the presence of noise
Cost and complexity

The higher the signal rate to achieve a given data rate, the greater
the cost
Reasons for Analog Modulation

Modulation of digital signals


When only analog transmission facilities are
available, digital to analog conversion required
Modulation of analog signals


A higher frequency may be needed for effective
transmission
Modulation permits frequency division
multiplexing
Basic Encoding Techniques

Analog data to analog signal


Amplitude modulation (AM)
Angle modulation


Frequency modulation (FM)
Phase modulation (PM)
Spectrum of AM signal
Amplitude Modulation

Transmitted power
 na
Pt  Pc 1 
2

2






Pt = total transmitted power in s(t)
Pc = transmitted power in carrier
Single Sideband (SSB)

Variant of AM is single sideband (SSB)



Advantages



Sends only one sideband
Eliminates other sideband and carrier
Only half the bandwidth is required
Less power is required
Disadvantages

Suppressed carrier can’t be used for synchronization
purposes
Pulse Modulation
Analogue modulated systems are quite widely used, because
of their simplicity.
An alternative to analogue modulated systems is Pulsed
systems.
This system is based on digital signals or pulses.
The basis of such a system is the use of a digital carrier
signal, which is modulated by an analogue signal.
There are various ways in which this can be achieved, giving
rise different systems.
Sampling of signals
An analogue signal is transmitted continuously in its entire form.
This need not be done provided certain conditions are satisfied.
Samples of the analogue signal may be transmitted at given
intervals of time.
The original signal may then be recovered at the receiving end
from the transmitted samples.
This technique is known as sampling and it underlies pulsed
systems.
Consider a train of signals, with a repetition frequency f and
period T where
1
f 
T
If the pulse train were amplitude modulated by the
analogue signal, the result will be pulses whose
amplitudes are samples of the analogue signal at time
intervals T.
If the amplitude modulated pulse train is then
analysed, its spectrum will consist of Fourier
components,
0, f , 2 f , 3 f ...
At each of this there will be a set of sum and difference frequencies
(lower and upper sidebands) due to each frequency component of
the analogue signal.
If W and f-W do not overlap then it is possible to separate the group of
frequencies at the receiving end.
This can be achieved by use of a low-pass filter with a cut-off
frequency f = W.
The separated frequencies are then those of the analogue signal
transmitted.
From this the following condition is derived
f W  W
f  2W
This means the repetition frequency must be at least twice the
highest frequency component in the analogue signal.
The minimum sampling frequency is then
f min  2W
This is also called the Nyquist rate.
If the sampling rate is less than 2W the lower sideband will
overlap the baseband and it will not be possible to separate them.
This effect is known as aliasing. It can be avoided by passing the
signal through a filter before sampling.
Telephone siganls range from 300 Hz to 3.4 kHz, the internationally
agreed sampling frequency is 8kHz. It means there is a guard band of
1.2kHz between the lower side band and the baseband.
Comment:
It means W has an upper limit
The technique can only be used if the bandwidth can be restricted to W
without destroying the essential information. To achieve this, bandlimited signals are used.
Sampling Theorem
Any function of time F t  whose highest
frequency is W Hz can be completely
determined by sampled amplitudes spaced at
1
time intervals 2W apart.
If a signal f(t) is sampled at regular intervals of time and at
a rate higher than twice the highest frequency, then the
samples contain all of the information of the original signal.
The function f(t) may be reconstructed from these samples
by the use of a low pass filter.
Sampler
An analogue sampler commonly known as the sample-andhold is used in sampling the input analogue signal voltage and
maintaining that voltage until the next sampling instant.
The FET (Field Effect Transistor) acts like a simple switch.
When turned "on," it provides a low-impedance path to
deposit the analogue sample voltage on capacitor.
The time that the FET is "on" is called the aperture or
acquisition time.
Essentially, the capacitor is the hold circuit. When the switch
FET is "Off," the capacitor does not have a complete path to
discharge through and therefore stores the sampled voltage.
The storage time of the capacitor is also called the conversion
time because it is during this time that the unit converts the
sample voltage to a digital code.
The acquisition time should he very short. This assures that a
minimum change occurs in the analogue signal while it is being
deposited across the capacitor.
If the input to the sampler is changing while it is performing the
conversion, distortion results. This distortion is called aperture
distortion.
Thus, by having a short aperture time and keeping the input to the
constant relatively constant, the sample-and-hold circuit reduces
aperture distortion.
If the analogue signal is sampled for a short period of time and the
sample voltage is held at constant amplitude during the conversion
time, this is called flat-top sampling.
If the sample time is made longer and the analogue-to-digital
conversion takes place with a changing analogue signal, this is called
natural sampling.
Natural sampling introduces more aperture distortion than flattop
sampling and requires a faster A/D converter.
Pulse Code Modulation
PCM is the most commonly used technique in digital
communications
Used in many applications:
Telephone systems
Digital audio recording
CD laser disks
voice mail
digital video etc.
They are a primary building block for advanced
communication systems
Pulse Code Modulation


Based on the sampling theorem
Each analog sample is assigned a binary
code


Analog samples are referred to as pulse
amplitude modulation (PAM) samples
The digital signal consists of block of n bits,
where each n-bit number is the amplitude of
a PCM pulse
Quantization

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Is the process of converting the sampled
signal to a binary value
Each voltage level will correspond to a
different binary number
The magnitude of the minimum step size is
called the resolution.
The error resulting from quantizing is called
the quantization noise. Its value is 1/2 the
resolution
Pulse Code Modulation
Dynamic Range
This is the ratio of the largest to smallest analogue signal
that can be transmitted.
Vmax
DR 
Vmin
But Vmin is the resolution and can be written as
Vmax
q  Vmin  n
2
It follows that
Vmax
DR 
 2n
Vmin
If this is expressed in decibels
Vmax
DR(dB)  20 log
 20 log 2n  20n log 2  6.02n
Vmin
DR(dB)  6n
From
DR  2n
It can be observed that the DR is the
Maximum binary number for a system. With one code used
for 0V which is not considered in calculating DR, it is
observed that
DR  2n  1
Example
Given a PCM system with the following parameters:
Maximum analog input frequency 3kHz
A maximum decoded voltage at the receiver of +/- 1.27V
A minimum dynamic range of 35dB.
Find the minimum sample rate
The number of bits required
The resolution
The quantization error
Quantization Noise

q
q
 error ( ) 
2
2
q
2
q
2
1  
1 2
  

d

Root mean square error
q  3 q
q q
2
3
2
The effective voltage
The noise power is

2
q

12 R
q
2 3
2
q

12
Reasons for Growth of Digital
Techniques

Growth in popularity of digital techniques
for sending analog data

Repeaters are used instead of amplifiers


TDM is used instead of FDM



No additive noise, can be used over long distances
No intermodulation noise
For a given bandwidth the signal/noise ratio is
superior
Conversion to digital signaling allows use of
more efficient digital switching techniques

Fits in well with other digital systems
Problems
Large bandwidth required. Might consider using optical fibres
Circuits for implementation are costly
uneconomical over short distances less than 5km.
Might consider using integrated circuits to deal with last two.