Data and signals.ppt

3.2
To be transmitted, data must be
transformed to electromagnetic signals.
Note
The basis of electronics is the electronic signal, an electric current that
represents information. There are two basic types of electrical signals:
analog and digital.

3.3
3-1 ANALOG AND DIGITAL
Data can be analog or digital. The term analog data refers
to information that is continuous; digital data refers to
information that has discrete states. Analog data take on
continuous values. Digital data take on discrete values.
 Analog and Digital Data
 Analog and Digital Signals
 Periodic and Nonperiodic Signals
Topics discussed in this section:

3.4
Analog and Digital Data
 Data can be analog or digital.
 Analog data are continuous and take
continuous values.
 Digital data have discrete states and take
discrete values.

3.5
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.

3.6
Figure 3.1 Comparison of analog and digital signals

3.7
3-2 PERIODIC ANALOG SIGNALS
In data communications, we commonly use periodic
analog signals and nonperiodic digital signals.
Periodic analog signals can be classified as simple or
composite. A simple periodic analog signal, a sine wave,
cannot be decomposed into simpler signals. A composite
periodic analog signal is composed of multiple sine
waves.
 Sine Wave
 Wavelength
 Time and Frequency Domain
 Composite Signals
 Bandwidth
Topics discussed in this section:

3.9
Figure 3.3 Two signals with the same phase and frequency,
but different amplitudes
Amplitude: the maximum extent of
a vibration or oscillation, measured
from the position of equilibrium.

3.10
Frequency and period are the inverse of
each other.
Note

3.11
Figure 3.4 Two signals with the same amplitude and phase,
but different frequencies

3.12
Table 3.1 Units of period and frequency

3.13
The power we use at home has a frequency of 60 Hz.
The period of this sine wave can be determined as
follows:
Example 3.1

3.14
The period of a signal is 100 ms. What is its frequency in
kilohertz?
Example 3.2
Solution
First we change 100 ms to seconds, and then we
calculate the frequency from the period (1 Hz = 10−3
kHz).

3.15
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.

3.16
If a signal does not change at all, its
frequency is zero.
If a signal changes instantaneously, its
frequency is infinite.
Note

3.17
Phase describes the position of the
waveform relative to time 0.
Note

3.18
Figure 3.5 Three sine waves with the same amplitude and frequency,
but different phases

3.19
A sine wave is offset 1/6 cycle with respect to time 0.
What is its phase in degrees and radians?
Example 3.3
Solution
We know that 1 complete cycle is 360°. Therefore, 1/6
cycle is

3.20
Figure 3.6 Wavelength and period

3.21
Figure 3.7 The time-domain and frequency-domain plots of a sine wave

3.22
A complete sine wave in the time
domain can be represented by one
single spike in the frequency domain.
Note

3.23
The frequency domain is more compact and
useful when we are dealing with more than one
sine wave. For example, Figure 3.8 shows three
sine waves, each with different amplitude and
frequency. All can be represented by three
spikes in the frequency domain.
Example 3.7

3.24
Figure 3.8 The time domain and frequency domain of three sine waves

3.25
Signals and Communication
 A single-frequency sine wave is not
useful in data communications
 We need to send a composite signal, a
signal made of many simple sine
waves.
 According to Fourier analysis, any
composite signal is a combination of
simple sine waves with different
frequencies, amplitudes, and phases.

3.26
Composite Signals and
Periodicity
 If the composite signal is periodic, the
decomposition gives a series of signals
with discrete frequencies.
 If the composite signal is nonperiodic, the
decomposition gives a combination of
sine waves with continuous frequencies.
A signal that does not repeats its pattern over a period is called aperiodic
signal or non periodic
A signal that repeats its pattern over a period is called periodic signal .

3.27
Figure 3.9 shows a periodic composite signal with
frequency f. This type of signal is not typical of those
found in data communications. We can consider it to be
three alarm systems, each with a different frequency.
The analysis of this signal can give us a good
understanding of how to decompose signals.
Example 3.4

3.28
Figure 3.9 A composite periodic signal

3.29
Figure 3.10 Decomposition of a composite periodic signal in the time and
frequency domains

3.30
Figure 3.11 shows a nonperiodic composite signal. It
can be the signal created by a microphone or a telephone
set when a word or two is pronounced. In this case, the
composite signal cannot be periodic, because that
implies that we are repeating the same word or words
with exactly the same tone.
Example 3.5
At same tone, signals cant be differentiated.

3.31
Figure 3.11 The time and frequency domains of a nonperiodic signal

3.32
Bandwidth and Signal
Frequency
 The bandwidth of a composite signal is
the difference between the highest and
the lowest frequencies contained in that
signal.

3.33
Figure 3.12 The bandwidth of periodic and nonperiodic composite signals

3.34
If a periodic signal is decomposed into five sine waves
with frequencies of 100, 300, 500, 700, and 900 Hz, what
is its bandwidth? Draw the spectrum, assuming all
components have a maximum amplitude of 10 V.
Solution
Let fh be the highest frequency, fl the lowest frequency,
and B the bandwidth. Then
Example 3.6
The spectrum has only five spikes, at 100, 300, 500, 700,
and 900 Hz (see Figure 3.13).

3.35
Figure 3.13 The bandwidth for Example 3.6

3.36
A periodic 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 frequencies of the
same amplitude.
Solution
Let fh be the highest frequency, fl the lowest frequency,
and B the bandwidth. Then
Example 3.7
The spectrum contains all integer frequencies. We show
this by a series of spikes (see Figure 3.14).

3.37

3.38
A nonperiodic composite signal has a bandwidth of 200
kHz, with a middle frequency of 140 kHz and peak
amplitude of 20 V. The two extreme frequencies have an
amplitude of 0. Draw the frequency domain of the
signal.
Solution
The lowest frequency must be at 40 kHz and the highest
at 240 kHz. Figure 3.15 shows the frequency domain
and the bandwidth.
Example 3.8

3.39

Data and signals.ppt

More Related Content

What's hot (20)

Similar to Data and signals.ppt (20)

More from AyeCS11 (11)

Recently uploaded (20)

Data and signals.ppt