School of Electrical, Electronics and

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• School of Electrical, Electronics and
• Computer Engineering
• University of Newcastle-upon-Tyne
• Baseband Digital Modulation
• Prof. Rolando Carrasco
• Lecture Notes
• University of Newcastle-upon-Tyne
• 2007

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Baseband digital information
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Bit-rate, Baud-rate and Bandwidth
denotes the duration of the 1 bit Hence Bit
rate
bits per second
All the forms of the base band signalling shown
transfer data at the same bit rate.
denotes the duration of the shortest
signalling element. Baud rate is defined as the
reciprocal of the duration of the shortest
signalling element.
Baud Rate
baud
In general Baud Rate ? Bit Rate
For NRZ Baud Rate Bit Rate
RZ Baud Rate 2 x Bit Rate
Bi-Phase Baud Rate 2 x Bit Rate
AMI Baud Rate Bit Rate
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Non Return to Zero (NRZ)
The highest frequency occurs when the data is
1010101010. i.e.
This sequence produces a square wave with
periodic time
Fourier series for a square wave,
If we pass this signal through a LPF then the
maximum bandwidth would be 1/T Hz, i.e. to just
allow the fundamental (1st harmonic) to pass.
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Non Return to Zero (NRZ) (Contd)
The data sequence 1010 could then be
completely recovered

Hence the minimum channel bandwidth
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Return to Zero (RZ)
Considering RZ signals, the max frequency occurs
when continuous 1s are transmitted.
.

This produces a square wave with periodic time
If the sequence was continuous 0s, the signal
would be V continuously, hence
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Bi-Phase
Maximum frequency occurs when continuous 1s or
0s transmitted.
This is similar to RZ with Baud Rate
2 x Bit rate


The minimum frequency occurs when the sequence is
10101010. e.g.
In this case

Baud Rate Bit rate
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Digital Modulation and Noise
The performance of Digital Data Systems is
dependent on the bit error rate, BER, i.e.
probability of a bit being in error.
Prob. of Error or BER,
Digital Modulation There are four basic ways of
sending digital data

• The BER (P) depends on several factors
• the modulation type, ASK FSK or PSK
• the demodulation method
• the noise in the system
• the signal to noise ratio

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Digital Modulation and Noise
Amplitude Shift Keying ASK
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Digital Modulation and Noise
Frequency Shift Keying FSK
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Digital Modulation and Noise
Phase Shift Keying PSK
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System Block diagram for Analysis
DEMODULATOR DETECTOR DECISION
For ASK and PSK
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Demodulator-Detector-Decision
FOR FSK
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Demodulator
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Demodulator Contd)

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Detector-Decision
- is the voltage difference between a 1
and 0.
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Detector-Decision (Contd)
ND is the noise at the Detector
input. Probability of Error,

Hence
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Probability density of binary signal
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Probability density function of noise
()
Using the change of variable
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This becomes
()
The incomplete integral cannot be evaluated
analytically but can be recast as a
complimentary error function, erfc(x), defined by
Equations () and () become
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It is clear from the symmetry of this problem
that Pe0 is identical to Pe1 and the probability
of error Pe, irrespective of whether a one or
zero was transmitted, can be rewritten in
terms of ?v v1 v0

• for unipolar signalling (0 and ?v)
• for polar signalling (symbol represented by
  voltage

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Detector-Decision (Contd)
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Detector-Decision (Contd)
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FM/ FSK Demodulation
One form of FM/FSK demodulator is shown below
In general VIN (t) will be
Where
is the input frequency (rad/sec)
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FM/ FSK Demodulation (Contd)
i.e
Thus there are two components
Component (1) is at frequency 2 fIN Hz and
component (2) is effectively a DC voltage if

is constant.
The cut-off frequency for the LPF is designed so
that component (1) is removed and component (2)
is passed to the output.
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FM/ FSK Demodulation (Contd)
The V/F characteristics and inputs are shown
below Analogue FM
Modulation Index
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FM/ FSK Demodulation (Contd)
The spectrum of the analogue FM signal depends on
and is given by
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Digital FSK
Normalized frequency Deviation ratio
The spectrum of FSK depends on h
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Digital FSK (Contd)
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FM/ FSK Demodulation (Contd)
Consider again the output from the demodulator
The delay
is set to
where
and
is the nominal carrier frequency
Hence

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FM/ FSK Demodulation (Contd)
The curve shows the demodulator F/V
characteristics which in this case is non linear.
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Practical realization of F/V process
The comparator is LIMITER which is a zero
crossing detector to give a digital input to
the first gate.
This is form of delay and multiply circuit
where the delay
is set by C and R with
CR
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Practical realization of F/V process (Contd)
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Practical realization of F/V process (Contd)
Consider now
?
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Practical realization of F/V process (Contd)
Plotting Vout versus
(Assuming A1)