pulse code modulation lecture 5. why a particular encoding technique digital data, digital signal...
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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 CompareEncoding Schemes Signal spectrum
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
Clocking 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
Pt = total transmitted power in s(t)
Pc = transmitted power in carrier
21
2a
ct
nPP
Single Sideband (SSB) Variant of AM is single sideband (SSB)
Sends only one sideband Eliminates other sideband and carrier
Advantages 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.
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.
Sampling of signals
Consider a train of signals, with a repetition frequency f and period T where
Tf
1
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,
...3 ,2 , ,0 fffAt 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
WWf Wf 2
This means the repetition frequency must be at least twice the highest frequency component in the analogue signal.
The minimum sampling frequency is then
Wf 2min 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, band-limited signals are used.
Sampling Theorem
Any function of time tF whose highestfrequency is W Hz can be completelydetermined by sampled amplitudes spaced at
time intervals W2
1 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.
An analogue sampler commonly known as the sample-and-hold is used in sampling the input analogue signal voltage and maintaining that voltage until the next sampling instant.
Sampler
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 communicationsUsed in many applications:
Telephone systemsDigital audio recordingCD laser disksvoice maildigital 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 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.
min
maxDRV
V
But Vmin is the resolution and can be written as
n
VVq
2max
min
It follows thatn
V
V2DR
min
max
If this is expressed in decibels
nnV
V n 02.62log202log20log20DR(dB)min
max
n6DR(dB)
From n2DR 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
12DR n
Example
Given a PCM system with the following parameters:Maximum analog input frequency 3kHzA maximum decoded voltage at the receiver of +/- 1.27VA minimum dynamic range of 35dB.
Find the minimum sample rateThe number of bits requiredThe resolutionThe quantization error
Quantization Noise
2)(
2
qerror
q
2
2
21q
q
dq
2
2
3
3
1q
12
2qRoot mean square
error
The effective voltage
32
q
The noise power is
R
q
12
2
Reasons for Growth of Digital Techniques
Growth in popularity of digital techniques for sending analog data Repeaters are used instead of amplifiers
No additive noise, can be used over long distances TDM is used instead of FDM
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.