3. An electric signal satisfying certain
requirements can be reproduced from an
appropriate set of instantaneous samples.
Sampling therefore makes it possible to
transmit a message in the form of pulse
modulation, rather than a continuous signal.
Usually the pulses are quite short compared
to the time between them, so a pulse
modulated wave has the property of being
“off” most of the time.
3
4. Second, the time interval between
pulses can be filed with sample values
from other signals, a process called
time-division multiplexing (TDM).
Pulse modulation offers two potential advantages
over CW modulation.
The transmitted power can be
concentrated into short bursts instead
of being generated continuously.
4
5. But pulse modulation has the
disadvantage of requiring very large
transmission bandwidth compared to the
message bandwidth. Consequently, the
methods of analog pulse modulation
discussed in this chapter are used
primarily as message processing for TDM
and/or prior to CW modulation.
5
8. x(t) = Input analog signal
S(t) = Switching function
Xs(t ) = Sampled signal
Sampling rate fs == 1/Ts Hz
Since s(t) is periodic, it can be written as a Fourier
series 8
12. The sampling operation has left the message
spectrum intact, merely repeating it periodically
in the frequency domain with a spacing of fs. The
first term of the spectrum equation is precisely
the message spectrum,attenuated by the duty
cycle c0 = fsτ = τ /Ts.
Two conditions obviously are necessary to
prevent overlapping spectral bands: the
message must be bandlimited, and the
sampling frequency must be sufficiently
great that fs – W ≥W. 12
15. The Fourier transform of a bipolar square wave
contains only only the odd harmonics of fs.
15
16. Note that Xs(f) contains no DC component
and only the odd harmonics of fs. Clearly,
we can’t recover x(t) by lowpass filtering.
Instead, the practical applications of bipolar
choppers involve bandpass filtering. If we
apply xs(t) to a BPF centered at some odd
harmonic nfs, the output will be
proportional to x(t) cos(nωst), a double-
sideband suppressed -carrier waveform
Thus, a bipolar chopper serves as a
balanced modulator. 16
21. Summary
Theorem of uniform (periodic) sampling
If a signal contains no frequency components for
|f|≥W, it is completely described by instantaneous
sample values uniformly spaced in time with
period Ts ≤1/2W. If a signal has been sampled at
the Nyquist rate or greater (fs ≥ 2W) and the
sample values are represented as weighted
impulses, the signal can be exactly reconstructed
from its samples by an ideal LPF of bandwidthB,
where W ≤B ≤ fs – W. 21
22. PULSE-AMPLITUDE MODULATION
The pulse amplitude varies in direct proportion
to the sample values of x(t).
The output of the sampler xs(t) is PAM signals
22
23. Flat-Top Sampling and PAM
PAM waveform obtained by the sample/hold
( S/H) technique 23
25. PULSE-TIME MODULATION
• Pulse-duration (PDM)
(also called) Pulse-width modulation (PWM)
Pulse-position modulation (PPM)
Time parameter of the pulse is being
modulated, and the pulses have constant
Amplitude. The pulse width or pulse
position varies in direct proportion to the
sample values of x(t).
25
27. The duration of the kth pulse in the PDM signal
in which the unmodulated duration t0
represents x(kTs)= 0 and the modulation
index µ controls the amount of duration
modulation.
27
28. in which the unmodulated position kTs + td
represents x(kTs) 0 and the constant t0
controls the displacement of the modulated
pulse.
The kth pulse in a PPM signal begins at time
28
31. The system employs a comparator and a sawtooth-wave
generator with period Ts. The output of the comparator is
zero except when the message waveform x(t) exceeds the
sawtooth wave, in which case the output is a positive
constant A. Hence, the comparator produces a PDM signal
with trailing-edge modulation of the pulse duration.
(Reversing the sawtooth results in leading-edge
modulation while replacing the sawtooth with a
triangular wave results in modulation on both edges.)
Position modulation is obtained by applying the PDM
signal to a monostable pulse generator that triggers on
trailing edges at its input and produces short output
pulses of fixed duration.
31
33. PCM is a digital transmission system with an
analog-to-digital converter (ADC) at the
input and a digital-to-analog converter
(DAC) at the output.
PCM Generation and Reconstruction
Generation system:
The analog input waveform x(t) is lowpass
filtered and sampled to obtain x(kTs ) .
33
34. A quantizer rounds off the sample values to
the nearest discrete value in a set of q
quantum levels. The resulting quantized
samples xq(kTs ) are discrete in time (by
virtue of sampling) and discrete in amplitude
(by virtue of quantizing).
PCM generation system; 34
36. Let the analog message be a voltage waveform
normalized such that │x(t)│ ≤ 1 V
Uniform quantization subdivides the 2-V peak-to-
peak range into q equal steps of height 2/q V
The quantum levels are then taken to be at
q is an even integer
The normalized quantization-level step size
36
38. Next, an encoder translates the quantized
samples into digital code words. The
encoder works with M-ary digits and
produces for each sample a codeword
consisting of v digits in parallel. Since there
are M˄v possible M-ary codewords with v
digits per word, unique encoding of the q
different quantum levels requires that M˄v≥
q. The parameters M, v, and q should be
chosen to satisfy the equality, so that
38
39. Each encoded sample is represented by a v-
digit output word, so the signaling rate
becomes r = vfs with fs ≥ 2W .
Therefore, the bandwidth needed for PCM
baseband transmission is
39
40. PCM receiver
The received signal may be contaminated by noise, but
regeneration yields a clean and nearly errorless
waveform if the signal-to-noise ratio (S/N)R is sufficiently
large. The DAC operations of serial-to-parallel
conversion, M-ary decoding, and sample-and-hold
generate the analog waveform xq(t). This waveform is a
“staircase” approximation of x(t), similar to flat-top
sampling except that the sample values have been
quantized. Lowpass filtering then produces the smoothed
output signal , which differs from the message x(t) to the
extent that the quantized samples differ from the exact
sample values x(kTs) .
40
41. Perfect message reconstruction is impossible
in PCM, even when random noise has no
effect. The ADC operation at the transmitter
introduces permanent errors that appear
at the receiver as quantization noise in the
reconstructed signal.
PCM receiver
41
45. DIGITAL CW MODULATION
A digital signal can modulate the amplitude,
frequency, or phase of a sinusoidal carrier wave. If
the modulating waveform consists of NRZ
rectangular pulses, then the modulated parameter
will be switched or keyed from one discrete
value to another.
Example
Binary amplitude-shift keying (ASK)
Binary frequency-shiftkeying (FSK)
Phase-shift keying (PSK)
45
50. )2sin()( ftVtv
•If the amplitude, V of the carrier is
varied proportional to the information
signal, a digital modulated signal is called
Amplitude Shift Keying (ASK)
•If the frequency, f of the carrier is varied
proportional to the information signal, a
digital modulated signal is called
Frequency Shift Keying (FSK)
Carrier Signal
50
51. •If the phase, θ of the carrier is varied
proportional to the information signal, a
digital modulated signal is called Phase
Shift Keying (PSK)
•If both the amplitude,V and the phase, θ
of the carrier are varied proportional to the
information signal, a digital modulated
signal is called Quadrature Amplitude
Modulation (QAM)
51
52. M-ary Encoding
• It is often advantageous to encode at a
level higher than binary where there are
more then two conditions possible.
• The number of bits necessary to produce a
given number of conditions is expressed
mathematically as
N = number of bits necessary M = number of symbols, level or
combinations possible with N bits.
MN 2log
52
53. • The rate of change of a signal on the
transmission medium after encoding and
modulation have occurred.
baud = 1/ts
baud = symbol rate (symbol per second)
ts = time of one signaling element (symbol
time (seconds)
Baud
53
54. Passband digital modulation has form
Bits encoded in amplitude An, phase θn, or
frequency θn=2π(fn-fc)t, which are constant
over a bit time Tb.
54
55. CONSTELLATION DIAGRAM
Graphical representation of the complex
envelope of each possible symbol state.
The x-axis represents the in-phase
component and the y-axis the quadrature
component of the complex envelope.
Thee distance between signals on a
constellation diagram relates to how
different the modulation waveforms are and
how easily a receiver can differentiate
between them. 55
57. Amplitude Shift Modulation
•The binary ASK waveform be generated
simply by turning the carrier on and off, a
process described as on-off keying (OOK).
•M-ary ASK waveform has M-1 discrete “on’’
amplitudes as well as the “off’’.
M-ary Signaling M symbols (states)
Logics 0, 1, 2, 3. …, M-1 States
57
58. Each symbol carries (Log2 M) bits
M-ary ASK signal represents binary data at
rate
r = Symbol rate rb= bite rate
The estimated transmission bit BT≈ r
BT ≈ rb/(Log2 M) 58
63. 63
Detectors for BASK: Coherent Receiver
Coherent detection requires the phase information
A coherent detector mixes the incoming signal with a
locally generated carrier reference
Multiplying the received signal r(t) by the receiver
local oscillator (say Accos(wct)) yields a signal with a
baseband component plus a component at 2fc
Passing this signal through a low pass filter eliminates
the high frequency component
The output of the LPF is sampled once per bit period T
64. Noncoherent Receiver
Does not require a phase reference at the receiver If
we do not know the phase and frequency of the
carrier, we can use a noncoherent receiver to recover
ASK signal
Envelope Detector
The simplest implementation of an envelope detector
comprises a diode rectifier and smoothing filter. fo is the carrier
frequency 64
65. Phase-shift keying (PSK)
The phase of the carrier signal is switched
between 2 (for BPSK) or more (for MPSK) in
response to the baseband digital data
The information is contained in the
instantaneous phase of the modulated carrier
Usually this phase is imposed and measured
with respect to a fixed carrier of known phase –
Coherent PSK
For binary PSK, phase states of 0o and 180o are
used 65
66. BPSK Waveform
Xc(t)
It display antipodal signalling.
I.e. symbols are equal and
Opposite to each other, unlike
ASK
Constellation Diagram
66
68. Xc(t)= Ac cos (ωc t + Øi)
0≤t≤Ts i=1, 2, …,M
Mi
M
i
ti ,....1
)1(2
)(
In MPSK, the phase of the carrier takes on
one of M possible values
M-ary PSK (MPSK)
68
70. Quadrature PSK (QPSK)
• Two BPSK in phase quadrature
• QPSK (or 4PSK) is a modulation technique
that transmits 2-bit of information using 4
states of phases
• For example
2-bit
Information
ø
00 0
01 π/2
10 π
11 3π/2
Each symbol
corresponds
to two bits
70
71. scQPSK Tti
M
i
tfActX
04,3,2,1,
)1(2
2cos)(
scQPSK Tti
M
i
tActx
04,3,2,1,
4
)1(2
cos)(
We can also have
Øi = 45⁰, 135⁰, 225⁰, or 315⁰
scQPSK Tti
M
i
tActx
04,3,2,1,
4
)1(2
cos)(
71
75. Frequency -Shift Keying
The instantaneous frequency of the carrier
signal is switched between two (or more)
values by the modulating digital data signal.
BFSK
75
77. There are two basic methods for generation
digital frequency modulation
FSK : The digital signal x(t) controls a switch
that selects the modulated frequency from a bank
of M oscillators. The modulated signal is
discontinuous at every switching instant. The
resultant output spectrum will contain relatively
large sidelobes which don’t carry any additional
information and thus waste bandwidth.
Discontinuities are avoided in continuous-
phase FSK (CPFSK) where x(t) modulates the
frequency of a single oscillator.
77
78. fc1 fcM
Digital frequency modulation: (a) FSK; (b)
continuous-phase FSK. The digital signal has M
logic states (0, 1, 2, …, M-1)
fc2
78
