Chapter Four.pdf ffhgfch fygbyd fehfhugd

University of Gondar
Institute of Technology
Electrical Engineering Department
By:- Habte Aregawi
Introduction to Communication
(EEng4116 )
Pulse and Digital Modulation Techniques

Contents
• Introduction of Digital Communication
• Sampling Techniques for Analog Modulation Systems
• Pulse Amplitude Modulation (PAM)
• Pulse Position Modulation (PPM)
• Pulse Duration Modulation (PDM)
• Quantization
• Pulse code Modulation (PCM)

Introduction To Digital Transmission
• Digital Transmission: discrete signals transmission.
• Analog Transmission: transmission of continuous wave signals
• Why Digitize Analog Sources
• Digital systems are less sensitive to noise, distortion, and interference.
• More flexibility through DSP (processing, service, etc)
• Fits to computer/ Data communications

Block Diagram of Digital Communication

Sampling Theorem
• Sampling: - is a process that analog signal is converted into a
corresponding sequence of samples in the time domain.
• The samples are usually spaced uniformly in time.
• The operation is basic to digital signal processing and digital
communications.
• For a procedure to have practical utility, it is necessary that we choose
the sampling rate properly,
• The sequence of samples uniquely defines the original analog signal.

Instantaneous Sampling (1 of 3)
• Suppose that we sample the signal g(t)
instantaneously and at a uniform rate,
once every 𝑇𝑠 seconds.
• We obtain an infinite sequence of
samples spaced denoted by g 𝒏𝑻𝒔 ,
• Where n is all possible integer values.
• 𝑇𝑠 sampling period, sampling rate
𝒇𝒔 =
𝟏
𝑻𝒔
• The ideal sampled signal g𝛿 𝑡
g𝜹 𝒕 = ෍
𝒏=−∞
∞
g 𝒏𝑻𝒔 𝜹 𝒕 − 𝒏𝑻𝒔

• From the definition of the delta, we recall that such an idealized function
has unit area.
• For G(f) is the Fourier transform of the original signal g(t), The Fourier
transform of pair of sampled signal is:
g𝜹 𝒕 ⇌ 𝒇𝒔 ෍
𝒎=−∞
∞
𝑮(𝒇 − 𝒎𝒇𝒔)
• Sampling theorem for strictly band-limited signals of finite energy:
I. It is completely described by instantaneous sample values uniformly spaced in time
with period 𝑇𝑠 < Τ
1 2𝑊
II. The signal can exactly recovered from a knowledge of its samples taken at the rate
of 𝑓𝑠 ≥ 2𝑊 samples per second.

• The sampling rate of 2𝑊 samples per second, for a signal bandwidth
of 𝑊 Hertz, is called the Nyquist rate
• Its reciprocal Τ
1 2𝑊(measured in seconds) is called the Nyquist
interval.

Pulse Amplitude Modulation (PAM) (1 of 5)
• It is the simplest and most basic form of analog pulse modulation.
• The amplitudes of regularly spaced pulses are varied in proportion to
the corresponding sample values of a continuous message signal
• The pulses can be of a rectangular form or some other appropriate
shape
• The dashed curve depicts the waveform of a
message signal m(t ),
• The sequence of amplitude modulated
rectangular pulses shown as solid lines
represents the corresponding PAM signal s(t).

• There are two operations involved in the generation of the PAM signal
1. Instantaneous sampling of the message signal m(t) every 𝑇𝑠 seconds where
the sampling rate 𝑓𝑠 = Τ
1 𝑇𝑠, is chosen in accordance to sampling theorem
2. Lengthening the duration of each sample to obtained some constant value T
• In digital circuit technology, these two operations are jointly referred
to as “sample and hold.”
• One important reason for intentionally lengthening the duration of
each sample is to avoid the use of an excessive channel bandwidth

• The PAM signal can be expressed as:
𝒔 𝒕 = ෍
𝒏=−∞
∞
m 𝒏𝑻𝒔 𝒉 𝒕 − 𝒏𝑻𝒔
• The ℎ 𝑡 is a standard rectangular pulse of unit amplitude and
duration 𝑇, defined as
ℎ 𝑡 =
1 0 < 𝑡 < 𝑇
1
2
𝑡 = 0, 𝑡 = 𝑇
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒𝑠

• The instantaneously sampled version of m(t) is given by
m𝜹 𝒕 = ෍
𝒏=−∞
∞
m 𝒏𝑻𝒔 𝜹 𝒕 − 𝒏𝑻𝒔
• Convolving m𝛿 𝑡 with the pulse ℎ 𝑡
𝒔 𝒕 = m𝜹 𝒕 ⋆ 𝒉 𝒕 = ෍
𝒏=−∞
∞
m 𝒏𝑻𝒔 𝒉 𝒕 − 𝒏𝑻𝒔
• Taking the Fourier transform of both sides
𝑆 𝑓 = M𝛿 𝑓 𝐻 𝑓 = 𝒇𝒔 ෍
𝒌=−∞
∞
𝑴 𝒇 − 𝒌𝒇𝒔 𝑯(𝒇)

* =

Reconstruction PAM Signals (1 of 3)
• First step, passing 𝒔 𝒕 through a low-pass
filter whose frequency response is defined.
• The spectrum of the resulting filter output is
equal to M 𝑓 𝐻 𝑓
• This output is equivalent to passing the
original message signal m 𝑡 through
another low-pass filter of transfer function
𝐻 𝑓 .
Amplitude response of reconstruction filter
Reconstructing PAM Signals

• Since using flat-top samples to generate a PAM signal, we have
introduced amplitude distortion as well as a delay of
𝑇
2
.
• The distortion caused by the use of referred to as the aperture effect.
• This distortion may be corrected by connecting an equalizer in cascade
with the low-pass reconstruction filter.
• The equalizer has the effect of decreasing the in-band loss of the
reconstruction filter as the frequency increases in such a manner as to
compensate for the aperture effect.
Ideally, amplitude
response of the
equalizer

• The noise performance of a PAM system
can never be better than baseband-signal
transmission.
• For transmission over long distances, PAM
would be used only as a means of message
processing for time-division multiplexing
• From which conversion to some other
form of pulse modulation is subsequently
made
Figure: Flat-top sampling

Time-division Multiplexing (TDM)

Pulse-Width Modulation (PWM) (1 of 2)
• Analog pulse modulation results when some attribute of a pulse varies continuously
in one-to-one correspondence with a sample value.
• A PWM waveform consists of a sequence pulse having a width proportional to the
values of the message signal at the sampling instants.
• If the message is 0 at the sampling time, the width of the PWM pulse is typically
(1/2)𝑇𝑠.
• Thus, pulse widths less than (1/2)𝑇𝑠 correspond to negative sample values, and pulse
widths greater than (1/2)𝑇𝑠 correspond to positive sample values.
• The maximum pulse width of the PWM pulses is exactly equal to the sampling
period 1∕𝑇𝑠.
• This form of modulation is also referred to Pulse-Duration Modulation(PDM) or
or pulse-length modulation

• PWM is seldom used in modern communications systems.
• However, PWM has found extensively for DC motor control in which
motor speed is proportional to the width of the pulses.
• Large amplitude pulses are therefore avoided.
• Since the pulses have equal amplitude, the energy in a given pulse is
proportional to the pulse width.
• The sample values can be recovered from a PWM waveform by
lowpass filtering
Pulse-Width Modulation (PWM) (2 of 2)

Illustration of Pulse Modulations

Pulse-Position Modulation (PPM) (1 of 3)
• A PPM signal consists of a sequence of pulses in which the pulse
displacement from a specified time reference is proportional to the
sample values of the information-bearing signal.
• In PDM, long pulses expend considerable power during the pulse
while bearing no additional information.
• If this unused power is subtracted from PDM, so that only time
transitions are preserved
• WE obtain a more efficient type of pulse modulation known as pulse-
position modulation (PPM).

• In PPM, the position of a pulse relative to its unmodulated time of occurrence is varied in
accordance with the message signal.
• Using the sample 𝑚(𝑛𝑇𝑠) of a message signal m(t) to modulate the position of the nth
pulse, we obtain the PPM signal
𝑠 𝑡 = ෍
−∞
∞
g(𝑡 − 𝑛𝑇𝑠 − 𝑘𝑝𝑚(𝑛𝑇𝑠))
• Where 𝑘𝑝is modulation sensitivity of the pulse-position modulator and g(t) denotes a
standard pulse of interest.
• Clearly, the different pulses constituting the PPM signal s(t) must be strictly
nonoverlapping;
• Sufficient condition for this requirement to be satisfied is to have
g 𝑡 = 0, 𝑡 >
𝑇𝑠
2
− 𝑘𝑝 𝑚 𝑡 𝑚𝑎𝑥 ⇒
𝑇𝑠
2
> 𝑘𝑝 𝑚(𝑡) 𝑚𝑎𝑥

• The closer 𝑘𝑝 𝑚(𝑡) 𝑚𝑎𝑥 is to one half the sampling duration Ts,
• The narrower must the standard pulse g(t) be in order to ensure that the
individual pulses of the PPM signal s(t) do not interfere with each other, and
• The wider will the bandwidth occupied by the PPM signal.
• The signal samples 𝑚(𝑛𝑇𝑠) can be recovered perfectly.

Pulse
generator
Sample and
hold circuit
Adder
Threshold
detector
Pulse
shaping
filter
Sawtooth
generator
Message
signal m(t)
u(t) v(t) i(t) PPM signal
s(t)
Figure: Block diagram of PPM generator.

Advantage of PPM
• In the context of noise performance, a PPM system represents the
optimum form of analog pulse modulation.
• PPM and FM systems exhibit a similar noise performance.

Reading Assignment
DETECTION OF PPM WAVES

Digital Pulse Modulation
• Digital modulation alleviate a trade-off of increased transmission
bandwidth and improved noise performance.
• There are two fundamental processes
• Sampling
• Quantizing
• Amplitude quantization is defined as the process of transforming the
sample amplitude m(nTs) of a message signal m(t) at time t = nTs
into a discrete amplitude v(nTs) taken from a finite set of possible
amplitudes.

• The quantization process is memoryless and instantaneous,
• The transformation at time t = nTs is not affected by earlier or later
samples of the message signal.
• The spacing between two adjacent representation levels is called a
quantum or step-size.

• The use of quantization introduces an error defined as the difference
between the input signal m and the output signal v.
• This error is called quantization noise.

Pulse-Code Modulation (PCM) (1 of 5)
• It is the most basic form of digital pulse modulation.
• In PCM a message signal is represented by a sequence of coded
pulses,
• Which is accomplished by representing the signal in discrete form in
both time and amplitude.
Lowpass
filter
Sampler Quantizer Encoder
Continuous time
message signal
PCM signal
Figure: Transmitter block diagram of PCM

• The low-pass filter prior to sampling is included to prevent aliasing of the
message signal.
• The quantizing and encoding operations are usually performed in the same
circuit, which is called an analog-to-digital converter.
• Sampling: The incoming message signal is sampled with a train of narrow
rectangular pulses so as to closely approximate the instantaneous sampling
process.
• Quantization: The sampled version of the message signal is then
quantized, thereby providing a new representation of the signal that is
discrete in both time and amplitude.

• ENCODING: process to translate the discrete set of sample values to
a more appropriate form of signal.
• Any plan for representing each of this discrete set of values as a
particular arrangement of discrete events is called a code
• One of the discrete events in a code is called a code element or
symbol.
• For example, the presence or absence of a pulse is a symbol.
• A particular arrangement of symbols used in a code to represent a
single value of the discrete set is called a codeword or character.

• In a binary code, each symbol may be either of two distinct values or
kinds, such as the presence or absence of a pulse.
• The two symbols of a binary code are customarily denoted as 0 and 1.
• The maximum advantage over the effects of noise in a transmission
medium is obtained by using a binary code,
• Because a binary symbol withstands a relatively high level of noise
and is easy to regenerate.
• Suppose that, in a binary code, each code word consists of R bits
(binary digit)
• R denotes the number of bits per sample.

• Then, using such a code, we may represent a total of 2𝑅 distinct
numbers.
• For example, a sample quantized into one of 256 levels may be
represented by an 8-bit code word
• LINE CODES: a binary stream of data takes on an electrical
representation.
• Anyone of several line codes can be used for the electrical
representation of a binary data stream.

Line codes
• It is in a line code that a binary stream of data takes on an electrical
representation.
• There are five commonly used line code signaling
1. Unipolar Nonreturn-to-Zero (NRZ)
2. Polar Nonreturn-to-Zero (NRZ)
3. Unipolar Return-to-Zero (RZ)
4. Bipolar Return-to-Zero (BRZ)
5. Split-Phase (Manchester Code)
• Return-to-zero implies that the pulse shape used to represent the bit
always returns to the 0 volts or the neutral level before the end of the bit.
• Nonreturn-to-zero indicates that the pulse does not necessarily return to
the neutral level before the end of the bit.

Unipolar or On-Off Keying (OOK)
1. Unipolar or On-Off Keying (OOK): The presence of pulse
represents a 1 and the absence of pulse represents a 0.
• There are two variations in Unipolar signaling
• Non Return to Zero (NRZ)
• Return to Zero (RZ)

Polar Signaling
2. Polar Signaling
• There are two methods of Polar Signaling
• Polar NRZ
• Polar RZ

Bi-polar Signaling
3. Bi-polar: is an encoding technique which has three voltage levels
namely +, - and 0. Such a signal is called as duo-binary signal.
• For a 1, the voltage level gets a transition from + to – or from – to +, having
alternate 1s to be of equal polarity. A 0 will have a zero voltage level.

Polar Nonreturn-to-Zero (NRZ)
Unipolar Nonreturn-to-Zero (NRZ)
Unipolar Return-to-Zero (RZ)
Bipolar Return-to-Zero (RZ)
Split-Phase (Manchester Code)

Differential PCM
• Samples of the bandlimited signal are correlated
• Previous samples give information about the next one.
• Example, If the previous samples are small, the next one will be small
with high probability.
• This can be used to improve PCM performance: to decrease the
number of bits used (and hence, the bandwidth)
• Main idea: quantize and transmit the difference between two adjacent
samples, rather than the samples.
• Since the adjacent samples are correlated, their difference is small and
requires less bits to transmit.

Delta Modulation (DM)
• In delta modulation (DM), an incoming message signal is oversampled
(i.e., at a rate much higher than the Nyquist rate).
• The oversampled purposely increase the correlation between adjacent
samples of the signal.
• In DM the sampling rate is much higher and in which the step-size Δ
after quantization is of a smaller value.
• Delta Modulation is a simplified form of DPCM technique

• When it is required to transmit binary data over band-pass
communication channels such as radio links or satellite channels,
• It is necessary to modulate the signal onto a carrier wave (usually
sinusoidal) with fixed frequency limits set by the particular channel.
• The modulation process corresponds to switching or keying the
amplitude, frequency, or phase of the carrier between either of two
possible values corresponding to binary symbols 0 and 1.
• This results in three basic signaling techniques, namely,
• Amplitude - Shift Keying ( ASK),
• Frequency - Shift Keying (FSK), and
• Phase - Shift Keying (PSK)
Introduction to digital modulation techniques

Amplitude - Shift Keying (ASK)
• For ASK, binary symbol 1 is represented by transmitting a sinusoidal carrier
wave of fixed amplitude and fixed frequency for the bit duration Tb seconds,
• whereas binary symbol 0 is represented by switching off the carrier for Tb
seconds.
• For example, an ASK signal may be generated by using the on-off form of
representation for the input binary data
• Then applying it together with the carrier to a product modulator.

Frequency - Shift Keying (FSK)
• In an FSK system, two sinusoidal waves of the same amplitude but
different frequencies are used to represent binary symbols 1 and 0.
• An FSK signal may be generated by using the bipolar form of
representation for the input binary data and
• Then applying it to a voltage controlled oscillator, or by switching
between two oscillators.

Frequency - Shift Keying (FSK)
• In a PSK system, a sinusoidal carrier wave of fixed amplitude and
fixed frequency is used to represent both symbols 1 and 0,
• Except that whenever symbol 0 is transmitted the carrier phase is
shifted by 180 degrees.
• For example, a PSK signal may be generated by representing the input
binary data in bipolar form and applying it, together with the carrier, to
a product modulator.

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