pulse modulation

1. TELECOMMUNICATIONS
ENGINEERING
INSTRUCTOR
Md Hasib Noor
Faculty of Engineering
Department of Electrical and Electronic
Engineering
Pulse Modulation

2.  Voice is analog in character moves in the form of waves.
 3-important wave-characteristics:
 Amplitude
 Frequency
 Phase
 Why Voice Digitization??
 Ensures better quality (than analog)
 Provides higher capacity (than analog)
 Deals with longer distance (than analog)
 Digitization is just a discrete electrical voltage.
 The amplitude of Electrical pulses can be varied to represent characteristics
of an analog voice signal.
Basic Concepts
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3.  PAM is the first step in digitizing an analog waveform.
 Establishes a set of discrete times at which the input signal waveform is sampled.
 The sampling process is equivalent to amplitude modulation of a constant
amplitude pulse train, thus, PAM.
 Nyquist Sampling Rate : The minimum sampling frequency required to extract all
information in a continuous, time-varying waveform.
 Nyquist Criterion: fs > 2*(BW)
where fs = sampling rate, BW = bandwidth of the input signal.
Figure 1: PAM
Pulse Amplitude Modulation (PAM)
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4.  The Nyquist frequency, named after electronic engineer Harry Nyquist, is half
of the sampling rate of a discrete signal processing system.
 It is sometimes known as the folding frequency of a sampling system.
 The “Nyquist frequency” should not be confused with the “Nyquist rate”,
which is the minimum sampling rate that satisfies the Nyquist sampling criterion
for a given signal or family of signals.
 The Nyquist rate is twice the maximum component frequency of the function
being sampled.
 For example, the Nyquist rate for the sinusoid at 0.6 fs is 1.2 fs, which means
that at the fs rate, it is being under sampled.
 Thus, Nyquist rate is a property of a continuous-time signal, whereas Nyquist
frequency is a property of a discrete-time system.
Nyquist rate & Nyquist frequency)
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5.  Spectrum of PAM Signal:
 The PAM spectrum can be derived by observing that a continuous train of impulses
has a frequency spectrum consisting of discrete terms at multiples of the sampling
frequency.
 The input signal amplitude modulates these terms individually. Thus a double-
sideband spectrum is produced about each of the discrete frequency terms in the
spectrum of the pulse train.
Pulse Amplitude Modulation (PAM)
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Figure 2: Spectrum of PAM Signal

6.  The original signal waveform is recovered by a low-pass filter designed to
remove all but the original signal spectrum.
 As shown in the figure 2, the reconstructive low-pass filter must have a cut-off
frequency that lies between BW and (fs – BW).
 Hence, separation is only possible if (fs – BW) is greater than BW (i.e., (fs > 2BW).
Pulse Amplitude Modulation (PAM)
6Figure 2: Spectrum of PAM Signal

7.  Foldover Distortion:
 If the input is under sampled (i.e. fs < 2BW), the original waveform cannot be
recovered without distortion.
 As indicated in figure 3, this output portion arises because the frequency
spectrum centered about the sampling frequency overlaps the original spectrum
and cannot be separated from the original spectrum by filtering.
 Since it is a duplicate of the input spectrum “folded” back on top of the desired
spectrum that causes the distortion, this type of sampling impairment is called
“foldover distortion.” Another term for this impairment is “aliasing”.
Pulse Amplitude Modulation (PAM)
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Figure 3: Foldover spectrum produced by under sampling an input

8.  PAM System:
 Complete PAM system includes a band-limiting filter (or anti-aliasing filter)
before sampling to ensure that no source related signals get folded back into the
desired signal bandwidth.
 End-to-End PAM system:
Pulse Amplitude Modulation (PAM)
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Figure 5

9.  Pulse Code Modulation (PCM):
 PCM is an extension of PAM wherein each analog sample is quantized into a
discrete value for representation as a digital code-word.
 PAM system can be converted to PCM if we add ADC* at the source and DAC**
at the destination.
Pulse Code Modulation (PCM)
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Figure 6: PCM
*ADC: analog to digital converter
**DAC: digital to analog converter

10.  Pulse amplitude modulation systems are not useful over long distance, for the
vulnerability of individual pulse amplitudes to noise, distortion and crosstalk.
 The susceptibility of amplitude may be eliminated by converting the PAM
samples into a digital format. (Using regenerative repeaters)
 A finite number of bits are used for coding PAM samples.
 n bit number can represent 2n samples.
 PAM samples amplitude can take on an infinite range of values.
 The PAM sample amplitude is quantized to the nearest of a range of discrete
amplitude levels.
Quantization and Binary Coding
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11.  Signal V is confined to a range
of VL and VH. This range is divided
into M (M=8) equal steps.
 The step size S is given by:
S = (VH - VL) / M
 The center of each steps locate the
quantization levels V0 , V1…V8.
 Quantized signal Vq takes any of
the quantized level value.
 A signal V is quantized to its nearest
quantization level.
 The convention followed to quantize the signal is Figure 7: The Process of Quantization
 Vq = V3 (if (V3 - S/2) ≤ V < (V3 + S/2)
 Vq = V4 (if (V4 - S/2) ≤ V < (V4 + S/2)
 Thus, the signal Vq makes quantum jump of step size S and at any instant of time
 the quantization error (V - Vq) has magnitude which is equal or less than S/2.
 The quantization in which the step size is uniform is called linear or uniform
quantization.
Quantization Process
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12.  Quantization brings about a certain amount of noise in immunity to the signal.
 Repeaters with quantizers are used after certain distance to control the
variation in instantaneous amplitude for attenuation and channel noise within ±
S/2.
 If instantaneous noise level is larger than S/2, error occurs in the quantization
level.
 The quantized signal is an approximate of the original signal.
 Quality can be increased by increasing the number of quantization levels.
 Sometimes increased levels introduces noise in the repeaters.
 The susceptibility to noise can be greatly minimized by resorting the digital
coding of the PAM sample amplitude.
 Each quantized level is represented by a code number and transmitted instead of
the level value.
 If binary arithmetic is used the number will be transmitted as a series of pulses.
 Such a system is called PCM System.
Quantization
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13.  Let’s assume: The analog signal is limited
in
its excursions to the range -4V
to +4V.
 The step size is 1 volt.
 Eight quantization levels are
used and are located at -3.5V,
-2.5V …., +3.5V. Code number
000 is assigned to -3.5V and so on.
 If the analog samples are
transmitted the 1.3, 2.7, 0.5 etc
will be transmitted.
 If the quantized values are transmitted
voltages 1.5, 2.5, 0.5 etc will be transmitted.
 In binary PCM the binary code patterns
101, 110,100 are transmitted.
Binary PCM
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Figure 8: Binary PCM - Features

14.  The functional diagram for PCM is
shown in the figure 9.
 The analog input V is band-limited to
3.4 KHz to prevent aliasing and sampled
at 8 KHZ.
 Samples are quantized to produce
PAM signals, and applied to encoder.
 Encoder generates a unique pulse
pattern for each quantized sample level.
 The quantizer and encoder together Figure 9: A PCM system for speech communication
work as Analog to Digital Converter (ADC).
 Receiver first separates the noise from the signals.
 A quantizer does it by determining the two voltage levels of the pulse.
 Then it regenerates the appropriate pulse depending on the decision.
PCM System
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15.  The regenerated pulse train is now fed to a decoder which assembles the pulse
pattern and generates a corresponding quantized voltage level.
 Quantizer and decoder work together as a Digital to Analog converter (DAC).
 The quantized PAM is now passed through a filter which rejects the frequency
components lying outside the baseband signal.
Figure 9: A PCM system for speech communication
PCM System
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16.  After sampling, the analogue amplitude value of each sampled (PAM) signal is
quantized into one of a number of L discrete levels. The result is a quantized
PAM signal.
 A code-word can then be used to designate each level at each sample time. This
procedure is referred to as “Pulse Code Modulation”.
Figure 10: Analogue to Digital Conversion
Analogue to Digital Conversion
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17.  After quantization, a digit is assigned to each of the quantized signal levels in such
a way that each level has a one-to-one correspondence with the set of real
integers. This is called digitization of the waveform.
 Each integer is then expressed as an n-bit binary number, called code-word, or
PCM word.
 The number of code-words, M , is related to n by: 2n= M.
Encoding
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18.  Quantization followed by digitization maps input amplitudes into PCM words.
 There are M integers, PCM words, or codewords to correspond to the M allowed
output amplitudes of the quantizer.
 Codebook is the set of all these M codewords.
Codeword
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19.  Analog to Digital:
Figure 11: Process of digitization
Analog to Digital
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20.  The quantized signal is an approximation to the original signal and some error.
 The instantaneous error e = V-Vq is randomly distributed within the range S/2 and
is called quantization error or noise.
 The mean square quantization error is S2.
 For linear quantization the probability distribution of the error is constant
within the ± (S/2).
Figure 12: Probability distribution of error due to linear quantization
Quantization Noise
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21.  The average quantization noise output power is given by the variance.
Where µ = mean, which is zero
for quantization noise.
 The range of quantization error ±(S/2) determines the limits of integration.
Quantization Noise
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de

22.  Signal to quantization noise ratio (SQR) is a good measure of performance of
a PCM system transmitting speech.
 If Vr is the r.m.s value of the input signal and the resistance level is 1 ohm, then
SQR is given by
Quantization Noise
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23.  If the input signal is a sinusoidal wave and Vm as the maximum amplitude, SQR
may be calculated from the full range sine wave as:
 Expressing S in terms of Vm and the number of steps, M, we have
Quantization Noise
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24.  Quantity 1.225M represents the signal to quantization noise voltage ratio for a
full range sinusoidal input voltage.
 M = 2n, where n is the number of bits used to code a quantization level.
Therefore:
 The table 1 is showing the values of SQR for different binary code word sizes for
sinusoidal input systems.
 Every additional code bits gives an increment of 6 dB in SQR.
Quantization Noise
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25.  Example: A sine wave with a 1-V maximum amplitude is to be digitized with a
minimum SQR of 30 dB. How many uniformly spaced quantization intervals are
needed, and how many bits are needed to encode each sample?
 Solution: Using Equation:
SQR = 7.78 + 20 log10 (Vm / S) Given,
The maximum size of a quantization interval is SQR = 30 dB
determined as: Vm = 1-V
S = (1) 10 –(30-7.78)/20
= 0.078 V
Thus 13 quantization intervals are needed for each polarity for a total of 26 intervals in
all. The number of bits required to encode each sample is determined as:
N = log2 (26) = 4.7 = 5 bits per sample
Quantization
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26. Uniform vs Non-Uniform
Quantization
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27.  An alternative is to first pass the speech signal through a nonlinearity before
quantizing with a uniform quantizer.
 The nonlinearity causes the signal amplitude to be Compressed.
 The input to the quantizer will have a more uniform distribution.
 At the receiver, the signal is Expanded by an inverse to the nonlinearity to avoid
signal distortion. .
 The process of compressing and expanding is called Companding.
Companding
Compression + Expansion Companding
)(ty)(tx )(ˆ ty )(ˆ tx
x
)(xCy = xˆ
yˆ
Compress Uniform Qauntize
Channel
Expand
Transmitter Receiver
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28. Companding
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29. Companding
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 Various compression–expansion characteristics can be chosen to implement a
compandor
 by increasing the amount of compression, we increase the dynamic range at the
expense of the signal-to-noise ration for large amplitude signals.
 There are two types of companding characteristics:
 µ-law Companding: used in North America and Japan
 A-law Companding: recommended by CCITT for Europe and most of the rest of the
world

30. Comparison between A-law
and mu law
• µ-Law has a larger dynamic range compared to A-law
• µ-Law has worse distortion with small signals compared to A-law
• µ-Law is used in North-America and Japan while A-law is commonly
used in Europe
• A-law takes precedence over µ-law with international calls
*** Please go through “Digital Communication” by John Bellamy for further
understanding for different Companding techniques

31.  (Differential PCM):
 A special kind of PCM technique that codes the difference between sample points to
compress the digital data.
 Because audio waves propagate in predictable patterns, DPCM predicts the next sample
and codes the difference between the prediction and the actual point.
 The differences are smaller numbers than the numerical value of each sample on the full
scale and thereby reduce the resulting bit-stream.
DPCM
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32.  This is a special kind of DPCM technique that requires much simpler circuitry
than PCM
 This technique is widely used for transmission of voice information where quality is
not of primary importance
 In this method, an analog waveform is tracked, using a binary 1 to represent a rise
in voltage, and a 0 to represent a drop.
 Transmits only one bit per sample.
 The Present sample value is compared with the previous sample value and this
result, whether the value is increased or decreased, is transmitted.
Delta Modulation
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33. Delta Modulation
Delta modulation components (transmitter)
integrator
converts the difference between the
input signal and the average of the
previous steps.
+
-
Previous comparator output
comparator referenced to 0 (two levels
quantizer), whose output is 1 or 0 if
the input signal is positive or negative.
+Δ
-Δ
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34. Delta demodulation components (receiver)
The demodulator is simply an integrator (like the one in
the feedback loop) whose output rises or falls with each
1 or 0 received. The integrator itself constitutes a low-
pass filter
Delta Modulation
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35. Delta Modulation
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• Slope overload distortion/noise - is caused by use of step size delta which is too small
to follow portions of waveform that has a steep slope. …Can be reduced by increasing
the step size.
• Granular noise - is caused by too large step size in signal parts with small slope. It can
be reduced by decreasing the step size.

36.  Adaptive DM:
A better performance can be achieved if the value of δ is not fixed. In adaptive delta
modulation, the value of δ changes according to the amplitude of the analog signal.
 Quantization Error:
It is obvious that DM is not perfect. Quantization error is always introduced in the
process. The quantization error of DM, however, is much less than that for PCM.
Adaptive Delta Modulation
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37. END
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