Transcript Signals - Barry University, Miami Shores, Florida

Signals
• The main function of the physical layer is moving
information in the form of electromagnetic signals across
a transmission media.
• Information can be in the form of data, voice, picture, and
so on.
• Generally the information usable to a person or
application is not in a form that can be transmitted over a
network.
• The information must be converted into a form that
transmission media can accept.
• Transmission media work by conducting energy along a
physical path.
• So a data stream of 1s and 0s must be turned into energy in
the form of electromagnetic signals.
• A signal is the physical representation of a certain
information.
• Signals and data are classified as analog or digital.
• Analog refers to something that is continuous- a set of
data and all possible points between.
• An example of analog data is the human voice.
• Digital refers to something that is discrete –a set of
specific points of data with no other points in between.
• An example of digital data is data stored in the memory of
a computer in the form of 0s and 1s.
• An analog signal is a continuous wave form that
changes smoothly. As the wave moves from a value A
to a value B, it passes through and includes an infinite
number of values along its path.
• A digital signal can have only a limited number of
defined values, often as simple as 1 and 0.
Comparison of analog and digital signals
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.
Periodic and aperiodic Signals
• Both analog and digital signals
can be of two forms: periodic
and aperiodic (non-periodic)
signals.
• A signal periodic signal consists
a continuously repeated pattern.
• The completion of one full
pattern is called a cycle.
• A period is defined as the
amount of time (expressed in
seconds) required to complete
one full cycle.
Periodic and aperiodic Signals
• An aperiodic signal changes
constantly without exhibiting a
pattern or cycle that repeats
over the time.
• Remark: By using Fourier
Transform it is possible to
decompose an aperiodic signal
into an infinite number of
periodic signals (see appendix
D)
Analog signals
• Analog signals can be classified
as simple or composite.
• A simple analog signal or sine
wave, cannot be decomposed
into simpler signals.
• A composite analog signal is
composed of multiple sine
waves.
• Sine waves can be fully described by three characteristics:
amplitude, period, frequency and phase.
• Amplitude: on a graph, the amplitude of a signal is the
value of the signal at any point on the wave. It is equal to
the vertical distance from a given point on the wave from
the horizontal axis.
• Amplitude is measured
In volts, amperes, or watts,
depending on the type of
Signal.
• Period and Frequency: period refers to the amount of
time, in seconds, a signal needs to complete one
cycle.
• Frequency refers to the number of periods in one
second. The frequency of a signal its number of
cycles per second.
• 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.
• If a signal does not change at all, its frequency is
zero. If a signal changes instantaneously, its
frequency is infinite.
Table 3.1 Units of periods and frequencies
Unit
Seconds (s)
Equivalent
1s
Unit
hertz (Hz)
Equivalent
1 Hz
Milliseconds (ms)
10–3 s
kilohertz (KHz)
103 Hz
Microseconds (ms)
10–6 s
megahertz (MHz)
106 Hz
Nanoseconds (ns)
10–9 s
gigahertz (GHz)
109 Hz
Picoseconds (ps)
10–12 s
terahertz (THz)
1012 Hz
Frequency and Period
• Period is the amount of time it takes a signal to complete
one cycle.
• Frequency is the number of cycles per second.
• Frequency=1/Period
• Period=1/Frequency
Example 1
Express a period of 100 ms in microseconds, and express
the corresponding frequency in kilohertz.
Solution
From Table 3.1 we find the equivalent of 1 ms.We make
the following substitutions:
100 ms = 100  10-3 s = 100  10-3  106 ms = 105 ms
Now we use the inverse relationship to find the
frequency, changing hertz to kilohertz
100 ms = 100  10-3 s = 10-1 s
f = 1/10-1 Hz = 10  10-3 KHz = 10-2 KHz
Phase
• The term phase describes the position of the waveform
relative to time zero.
• The phase is measured in degrees or radians (360 degrees is 2p
radians)
TIME AND FREQUENCY DOMAINS
•Time-domain representation
•Frequency-domain representation
Time and frequency domains
Time and frequency domains (continued)
Periodic Composite Signals
• A single-frequency sine wave is not useful in data
communications; we need to change one or more of its
characteristics to make it useful.
• According to Fourier analysis, any composite signal can
be represented as a combination of simple sine waves
with different frequencies, phases, and amplitudes.
Frequency spectrum comparison
Note: Direct current (DC) component
Frequency Spectrum and Bandwidth
• The frequency spectrum of a signal is the collection of all
the component frequencies it contains and is shown using a
frequency-domain graph.
• The bandwidth of a signal is the width of the frequency
spectrum, i.e., bandwidth refers to the range of component
frequencies.
• To compute the bandwidth, subtract the lowest frequency
from the highest frequency of the range.
Bandwidth
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.
Solution
B = fh - fl = 900 - 100 = 800 Hz
The spectrum has only five spikes, at 100, 300, 500, 700,
and 900 (see Figure 13.4 )
Example 3
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.
Solution
B = fh - fl
20 = 60 - fl
fl = 60 - 20 = 40 Hz
Example 4
Composite signals and transmission
media
• A medium may pass some
frequencies and may block
others. This means that when
we send a composite signal,
containing many frequencies, at
one end of the transmission
medium, we may not receive
the same signal at the other end.
A digital signal is a composite signal with an infinite bandwidth.
Composite signals and transmission
media
• The range of frequencies that a medium can pass is called
its bandwidth.
• The bandwidth is a property of a medium: It is difference
between the highest and the lowest frequencies that the
medium can satisfactorily pass.
• If bandwidth of a medium does not mach the spectrum of a
signal, some of the frequencies are lost.
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?
Solution
The answer is definitely no. Although the signal can have
the same bandwidth (1000 Hz), the range does not
overlap. The medium can only pass the frequencies
between 3000 and 4000 Hz; the signal is totally lost.
Digital Signals
• Most of the digital signals are aperiodic and, thus period or
frequency is not appropriate.
• Bit interval ( instead of period) and Bit rate (instead of
frequency)
• The bit interval is the time required to send one single bit.
• The bit rate is the number of bit intervals in one second,
usually expressed in bits per second (bps).
Example 6
A digital signal has a bit rate of 2000 bps. What is the
duration of each bit (bit interval)
Solution
The bit interval is the inverse of the bit rate.
Bit interval = 1/ 2000 s = 0.000500 s
= 0.000500 x 106 ms = 500 ms
Digital Signals
• A digital signal is a composite signal with
an infinite bandwidth.
• It is possible to send digital data through a
band-limited medium, such as a telephone
line.
• What is the minimum required bandwidth B
in Hertz if we want to send n bps?
•The bit rate and the bandwidth are proportional to each
other.
•The analog bandwidth of a medium is expressed in
hertz; the digital bandwidth, in bits per second.
n<=2B ( n in bps and B in Hertz)
Bit
Rate
Harmonic
1
Harmonics
1, 3
Harmonics
1, 3, 5
Harmonics
1, 3, 5, 7
1 Kbps
500 Hz
2 KHz
4.5 KHz
8 KHz
10 Kbps
5 KHz
20 KHz
45 KHz
80 KHz
100 Kbps
50 KHz
200 KHz
450 KHz
800 KHz
Low-pass and band-pass