Signals can be either analog or digital. Analog signals are continuous and can have any value within a range, while digital signals are discrete and can only have a limited set of values. Data is also either analog or digital - analog data varies continuously while digital data takes on discrete states of 0s and 1s. Signals can be transmitted through various media but will experience impairments like attenuation (loss of power), distortion (change in shape), and noise (unwanted signals) during transmission. Methods like encoding and noise reduction are used to combat these impairments.

1. Data and Signals

2. 3.2
To be transmitted, data must be
transformed to electromagnetic signals.
Note

3. 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:

4. 3.4
Note
Data can be analog or digital.
Analog data are continuous and take
continuous values.
Digital data have discrete states and take
discrete values.

5. Signals
• Analog Signal
• An analog signal is a continuous wave denoted by a sine wave and may vary in
signal strength (amplitude) or frequency (time).
• Digital Signal
• A digital signal is described as using binary (0s and 1s), and therefore, cannot take on any
fractional values.

6. 3.6
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.
Note

7. 3.7
Figure 3.1 Comparison of analog and digital signals

8. Both Analog and Digital signals can take on of
two forms:
• Periodic Signal
• Aperiodic Signal
3.8

9. 3.9
In data communications, we commonly use
periodic analog signals and nonperiodic
digital signals.
Note

10. 3.10
3-2 PERIODIC ANALOG 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:

11. 3.11
Figure 3.2 A sine wave

12. A sine wave can be represented by 3 parameters:
• Peak amplitude
• Frequency
• Phase
3.12

13. 3.13
Figure 3.3 Two signals with the same phase and frequency, but different amplitudes

14. 3.14
The voltage of a battery is a constant; this constant value can be considered a sine wave.
For example, the peak value of an AA battery is normally
1.5 V.
Example 3.2

15. 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 1 sec.
OR
Frequency of the signal is the no. of times a signal makes a complete cycle
within a given time frame.
3.15

16. 3.16
Frequency and period are the inverse of
each other.
Note

17. 3.17
Figure 3.4 Two signals with the same amplitude and phase,
but different frequencies

18. 3.18
Table 3.1 Units of period and frequency
Period Frequency

19. 3.19
The power we use at home has a frequency of 60 Hz. The period of this sine wave can be
determined as follows:
Example 3.3

20. 3.21
The period of a signal is 100 ms. What is its frequency in kilohertz?
Example 3.5
Solution
First we change 100 ms to seconds, and then we calculate the frequency from the period
(1 Hz = 10−3 kHz).

21. 3.22
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.
Note

22. 3.23
If a signal does not change at all, its
frequency is zero.
If a signal changes instantaneously, its
frequency is infinite.
Note

23. Time and Frequency Domains
• A signal can be represented as a function of time, i.e. it varies with
time.
• However, it can be also expressed as a function of frequency, i.e. a
signal can be considered as a composition of different frequency
components.
• Thus, a signal has both time-domain and frequency domain
representation.
3.30

24. Time-Domain and Frequency Domain plot
• Time-Domain plot shows changes in signal amplitude w.r.t time.
• Frequency Domain plot show the relationship between amplitude
and frequency. This plot is only concerned with the peak value and
the frequency.
3.31

25. 3.32
Figure 3.7 The time-domain and frequency-domain plots of a sine wave

26. 3.33
A complete sine wave in the time domain
can be represented by one single spike in
the frequency domain.
Note

27. 3.34
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

28. 3.35
Figure 3.8 The time domain and frequency domain of three sine waves

29. 3.36
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.
Note

30. 3.37
According to Fourier analysis, any
composite signal is a combination of
simple sine waves with different
frequencies, amplitudes, and phases.
Note

31. 3.38
The bandwidth of a composite signal is
the difference between the
highest and the lowest frequencies
contained in that signal.
Note

32. 3.39
Figure 3.12 The bandwidth of periodic and nonperiodic composite signals

33. 3.40
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 3.10
The spectrum has only five spikes, at 100, 300, 500, 700,
and 900 Hz (see Figure 3.13).

34. 3.41
Figure 3.13 The bandwidth for Example 3.10

35. 3.42
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 3.11
The spectrum contains all integer frequencies. We show
this by a series of spikes (see Figure 3.14).

36. 3.43
Figure 3.14 The bandwidth for Example 3.11

37. 3.44
3-3 DIGITAL SIGNALS
A digital signal refers to an electrical signal that is converted into a pattern
of bits.
For example, a 1 can be encoded as a positive voltage and a 0 as zero
voltage.

38. 3.45
3-4 TRANSMISSION IMPAIRMENT
Signals travel through transmission media, which are not perfect. The imperfection causes
signal impairment. This means that the signal at the beginning of the medium is not the
same as the signal at the end of the medium. What is sent is not what is received. Three
causes of impairment are attenuation, distortion, and noise.
Attenuation
Distortion
Noise
Topics discussed in this section:

39. 3.46
Figure 3.25 Causes of impairment

40. Attenuation
• Attenuation means a loss of energy
• Attenuation is measured in decibels(dB). It measures the relative
strengths of two signals or one signal at two different point.
• Attenuation(dB) = 10log10(P2/P1)
P1 is power at sending end and P2 is power at receiving end.

41. 3.48
Figure 3.26 Attenuation

42. 3.49
Suppose a signal travels through a transmission medium
and its power is reduced to one-half. This means that P2
is (1/2)P1. In this case, the attenuation (loss of power)
can be calculated as
Example 3.26

43. Solution of Example 3.26

44. 3.51
A signal travels through an amplifier, and its power is
increased 10 times. This means that P2 = 10P1 . In this
case, the amplification (gain of power) can be calculated
as
Example 3.27

45. Solution of Example 3.27

46. Distortion
• Distortion means signal changes its form or shape.

47. Noise
• The random or unwanted signal that mixes up with the original signal
is called noise.
• There are several types of noise such as :
• Induced noise
• Crosstalk noise
• Thermal noise and
• Impulse noise

48. 3.55
Figure 3.29 Noise

49. Signal-to-Noise Ratio (SNR)
• It is a measure that compares the level of a desired signal to the level
of background noise.
• SNR is defined as the ratio of average signal power to the average
noise power, often expressed in decibels.
• SNR = AVG SIGNAL POWER / AVG NOISE POWER

50. 3.57
The power of a signal is 10 mW and the power of the
noise is 1 μW; what are the values of SNR and SNRdB ?
Example

51. Solution
• The values of SNR and SNRdB can be calculated as follows:

52. Data Rate
• Nyquist
• Shannon