Outline

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Outline
Analog and Digital Data Analog and Digital
Signals Amplitude Modulation (AM) Frequency
Modulation (FM)
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What is a Signal ?
Signals can be analog or digital. Analog signals
can have an infinite number of values in a range
digital signals can have only a limited number of
values.
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Periodic Signals
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Aperiodic Signals
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Analog and Digital Signals
In data communication, we commonly use periodic
analog signals and aperiodic digital signals.
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Periodic signal Sine Wave Period(T)
Frequency(F)
Peak Amplitude
T 1 / F
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Frequency
Frequency is the rate of change with respect to
time. Change in a short span of time means high
frequency. Change over a long span of time means
low frequency.
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Frequencies
Unit Equivalent Unit Equivalent
Seconds (s) 1 s hertz (Hz) 1 Hz
Milliseconds (ms) 103 s kilohertz (KHz) 103 Hz
Microseconds (ms) 106 s megahertz (MHz) 106 Hz
Nanoseconds (ns) 109 s gigahertz (GHz) 109 Hz
Picoseconds (ps) 1012 s terahertz (THz) 1012 Hz
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Example 1
Express a period of 100 ms in microseconds, and
express the corresponding frequency in kilohertz.
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Phase
Phase describes the position of the waveform
relative to time zero.
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Example 2
A sine wave is offset one-sixth of a cycle with
respect to time zero. What is its phase in
degrees and radians?
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Time-Domain Signal Representation

• where
• A Amplitude
• f frequency
• ? phase

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An analog signal is best represented in the
frequency domain.
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Time-Frequency Domain
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Time-Frequency Domain
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Time-Frequency Domain
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Examples
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Fourier Decomposition for Periodic Signals
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Example(1)
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Example(2)
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Example(3)
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Frequency Content of a Square Wave
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Figure 4-19
Harmonics of a Digital Signal
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Transmission Medium Imperfection
The bandwidth is a property of a medium It is
the difference between the highest and the lowest
frequencies that the medium can satisfactorily
pass.
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Frequency Response of a Medium
Signal frequency content
Frequency response of the medium
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Example 3
If a periodic signal is decomposed into five sine
waves with frequencies of 100, 300, 500, 700,
and 900 Hz, what is the bandwidth? Draw the
spectrum, assuming all components have a maximum
amplitude of 10 V.
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Example 4
A signal has a bandwidth of 20 Hz. The highest
frequency is 60 Hz. What is the lowest frequency?
Draw the spectrum if the signal contains all
integral frequencies of the same amplitude.
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Example 5
A signal has a spectrum with frequencies between
1000 and 2000 Hz (bandwidth of 1000 Hz). A medium
can pass frequencies from 3000 to 4000 Hz (a
bandwidth of 1000 Hz). Can this signal faithfully
pass through this medium?
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Digital Signals
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Bit rate (R) period of a bit (T)
The capacity of a data communication system can
be expressed in terms of the number of data bits
sent per second in time. bits per second or
(bits/sec)
This is also refers to the data rate (R) of the
system speed of transmission.
The period of data bit is called bit interval.
If the period of a data bit is T then R is the
inverse of T.
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Example 6
A digital signal has a bit rate of 2000 bps. What
is the duration of each bit (bit interval)
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Transmission Impairment
Attenuation Distortion Noise
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Attenuation
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Example 12
Imagine a signal travels through a transmission
medium and its power is reduced to half. This
means that P2 1/2 P1. In this case, the
attenuation (loss of power) can be calculated as
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Example 13
Imagine a signal travels through an amplifier and
its power is increased ten times. This means that
P2 10 P1. In this case, the amplification
(gain of power) can be calculated as
10 log10 (P2/P1) 10 log10 (10P1/P1) 10
log10 (10) 10 (1) 10 dB
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Example 14
One reason that engineers use the decibel to
measure the changes in the strength of a signal
is that decibel numbers can be added (or
subtracted) when we are talking about several
points instead of just two (cascading). In Figure
3.22 a signal travels a long distance from point
1 to point 4. The signal is attenuated by the
time it reaches point 2. Between points 2 and 3,
the signal is amplified. Again, between points 3
and 4, the signal is attenuated. We can find the
resultant decibel for the signal just by adding
the decibel measurements between each set of
points.
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dB 3 7 3 1
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Distortion
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Noise
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Analog Modulation
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Amplitude Modulation
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Amplitude Modulation
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Amplitude Modulation
The total bandwidth required for AM can be
determined from the bandwidth of the audio
signal rule-of thumb BWt 2 x BWm.
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AM band allocation
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Example 13
We have an audio signal with a bandwidth of 4
KHz. What is the bandwidth needed if we modulate
the signal using AM?
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Frequency Modulation
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Frequency Modulation
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Frequency Modulation
The total bandwidth required for FM can be
determined from the bandwidth of the audio
signal rule-of thumb BWt 10 x BWm.
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Frequency Modulation
The bandwidth of a stereo audio signal is usually
15 KHz. Therefore, an FM station needs at least a
bandwidth of 150 KHz. The FCC requires the
minimum bandwidth to be at least 200 KHz (0.2
MHz).
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FM Band Allocation
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Example 14
We have an audio signal with a bandwidth of 4
MHz. What is the bandwidth needed if we modulate
the signal using FM?
Solution
An FM signal requires 10 times the bandwidth of
the original signal BW 10 x 4
MHz 40 MHz
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Tutorial and Examples
1- Describe the three characteristics of a sine
wave.
a. amplitude, b. frequency/period, c. phase
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Tutorial and Examples
2- Describe a sine signal using the unit circle.
where x is in radians.
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Tutorial and Examples
2- Describe a cosine signal using the unit
circle.
where x is in radians.
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Tutorial and Examples
3-What are the amplitude, phase, and frequency
characteristics of the cosine signal that is
shown below.
Amplitude 10 Frequency100 Hz Phase ?/3
radians60 degrees
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Tutorial and Examples
4-What is the Fourier transform of the signal
that is shown below.
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Properties of Dirac-Delta functions
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x(t)
Ac
t
0
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Tutorial and Examples
5-What is the Fourier transform of the cosine
signal shown below?
Eulers Equations
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To prove Eulers equations
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Hence, the Fourier transform of