CHAP 3. DATA AND SIGNALS

What is the difference between analog and digital signals?

(1) An analog signal is a continuously varying signal. Digital

signal has discrete values.

(2) An analog signal has many levels of intensity over a period

of time. A digital signal has only a limited number of

defined values.

What are periodic and non-periodic signals?

(1) A periodic signal completes a pattern in a definite time frame called a period. Or, we can

say that a periodic signal repeats itself after equal intervals of time.

(2) The completion of a pattern is a cycle.

(3) A non-periodic or aperiodic signal does not repeat itslef after equal intervals of time.

(4) Both analog and digital signals can be periodic or non-periodic signals

Define the terms: time domain, and frequency domain

(1) A time-domain plot shows the changes in amplitude of a signal with respect to time. It is

an amlitude – vs – time plot. The continuous sine wave that is shown is an example of a

time domain plot. Phase is not shown on a time-doamin graph.

(2) A frequency-domain plot shows the changes in amplitude with frequency. Such a plot

shows only the peak value and the frequency. In such a graph we donot show the changes

in amplitude during one period.

(3) The frequency domain is easier to plot and contains the information present in the time

domain plot. We can also see the frequencies at which the values of amplitude raech their

maxima.

(4) A complete sine wave is represented by one spike. The position of the spike shows the

frequency; its height shows the peak amplitude.

(5) The frequency domain is more compact when we are dealing with more than one sine

wave.

Prof. Mukesh N Tekwani [9869 488 356]

Page 2 of 10 Chap 3 – Data & Signals

What is a composite signal?

(1) A single sine wave can not carry any meaningful information as it has just a single

frequency.

(2) A composite signal is made up of many sine waves of different frequencies. These waves

may also have different amplitudes and phases.

(3) According to Fourier analysis, any composite signal is a combination of simple sine

waves of different frequencies, amplitudes and phases.

(4) A composite signal can be periodic or nonperiodic.

(5) A periodic composite signal can be decomposed into a series of simple sine waves with

discrete frequencies that have integer values (1, 2, 3, and so on).

(6) A nonperiodic composite signal can be decomposed into a combination of an infinite

number of simple sine waves with continuous frequencies (frequencies that have real

values).

(7) A composite signal can be decomposed into its constituent signals.

A composite periodic signal

(8) The above signal when decomposed looks as shown below:

From the decomposed signal, we observe the following:

(i) The amplitude of the sine wave with frequeny f is the same as the peak amplitude of

the composite signal. This frequency f is called the fundamental frequeny or first

harmonic.

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Chap 1 – Introduction Page 3 of 10

(ii) The amplitude of the signal with frequeny 3f is 1/3rd

of that of the first. This

frequency of 3f is called the third harmonic.

(iii) The amplitude of the signal with frequency 9f is 1/9th

of that of the first. This

frequency is the 9th

harmonic.

(iv) The frequncy decomposition is discrete. The decomposed signal has frequencies of f,

3f and 7f. All these are integral values. We donot find frequencies such as 1.2f, etc.

Thus, the frequency domain of a periodic composite signal is made up of discrete

spikes or values.

The time and frequency domains of periodic and nonperiodic digital signals

Define the term bandwidth

(1) The range of frequencies contained in a composite signal is its bandwidth.

(2) The bandwidth is the difference between two frequencies. For example, if a composite

signal contains frequencies between 1000 and 5000, its bandwidth is 5000 - 1000, or 4000

Hz as shown below.

(3) In the diagram below we have a nonperiodic signal with the frequency range 1000 to

5000 Hz. The bandwidth is again 4000 Hz but the frequencies are continuous.

Prof. Mukesh N Tekwani [9869 488 356]

Page 4 of 10 Chap 3 – Data & Signals

What is a digital signal?

(1) A digital signal is used to represent data. A binary 1 can be encoded with a positive

voltage while the binary 0 can be encoded with the zero voltage.

(2) A digital signal can have more than two levels. In such a case we can send more than one

bit per level.

(3) We can send 1 bit per level in the first case and 2 bits per level in the second case. If a

signal has L levels, then each level requires log2L bits.

(4) Most digital signals are aperiodic. Therefore frequency and time period are not

appropriate characteristics.

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Chap 1 – Introduction Page 5 of 10

(5) The characteristics that are used to describe digital signals are : bit interval (instead of

period) and bit rate (instead of frequency).

(6) Bit interval is defined as the time required to send one bit.

(7) Bit rate is the number of bit intervals per second. It can also be defined as the number of

bits sent in one second. Units: bits per sec (bps)

(8) Bit length is the distance one bit occupies on the transmission medium. This is analogous

to the concept of wavelength for analog waves. Bit length = propagation speed x bit

duration.

How is decomposition of a digital signal achieved?

(1) A digital signal can be decomposed into an infinite number of simple sine waves called

harmonics.

(2) Each of these sine waves has a different frequency, amplitude and phase.

(3) Fourier analysis is used to decompose a digital signal.

(4) If the digital signal is periodic, the decomposed signal has a frequency domain

representation with an infinite bandwidth and discrete frequencies.

(5) If the digital signal is non-periodic, the decomposed signal still has an infinite bandwidth,

but the frequencies are continuous.

(6) A periodic signal has discrete frequencies while the non-periodic signal has continuous

frequencies.

What is meant by transmission impairment?

Explain the three types of transmission impairment.

(1) The transmission medium through which signals travel is not perfect. This imperfection

of the medium causes impairment of the signal.

(2) Impairment of a signal means that the signal quality at the beginning of the medium is not

the same as that at the end. Usually there is a deterioration in the quality of signal, as it

travels through the medium.

(3) The causes of impairment are:

a. Attenuation

b. Distortion

c. Noise

(4) Attenuations: Attenuation means a loss of energy. When a signal travels through a

medium, it loses some of its energy in overcoming the resistance of the medium. To

compensate for this loss, amplifiers are used to amplify the signal.

The loss or gain in signal strength is measured in units of decibel. The decibel (dB)

measures the relative strengths of two signals or one signal at two different points. The

decibel is negative if a signal is attenuated and positive if a signal is amplified.

dB = 10 log10 (P2 / P1)

P1 and P2 are the powers at points 1 (beginning of medium) and 2 (end of medium)

respectively.

Prof. Mukesh N Tekwani [9869 488 356]

Page 6 of 10 Chap 3 – Data & Signals

Example 1:

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

A loss of 3 dB (–3 dB) is equivalent to losing one-half the power.

Example 2:

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

Why is decibel unit used?

Decibel unit is used because these numbers can be added (or subtracted) when we are

measuring changes at several points (cascading). In Figure below a signal travels from

point 1 to point 4. In this case, the decibel value can be calculated as

(5) Distortion: Distortion means that the signal changes its form or shape. Distortion can

occur in a composite signal made of different frequencies. Each signal component has its

own propagation speed through a medium and, therefore, its own delay in arriving at the

final destination. Differences in delay may create a difference in phase if the delay is not

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Chap 1 – Introduction Page 7 of 10

exactly the same as the period duration. In other words, signal components at the receiver

have phases different from what they had at the sender. The shape of the composite signal

is therefore not the same.

(6) Noise: Any unwanted signal is called noise. Several types of noise, such as thermal noise,

induced noise, crosstalk, and impulse noise, may corrupt the signal.

a. Thermal noise is the random motion of electrons in a wire which creates an extra

signal not originally sent by the transmitter.

b. Induced noise comes from sources such as motors and appliances. These devices

act as a sending antenna, and the transmission medium acts as the receiving

antenna.

c. Crosstalk is the effect of one wire on the other. One wire acts as a sending

antenna and the other as the receiving antenna.

d. Impulse noise is a spike (a signal with high energy in a very short time) that

comes from power lines, lightning, and so on.

Signal-to-noise Ratio:

The SNR is defined as: the ratio of average signal power to the average noise power.

The SNR ratio indicates the ratio of the wanted signal to the unwanted signal (white

noise). A high value of SNR means that the signal is less corrupted by noise.

Since SNR is the ratio of two powers, it is described in decibel units as follows:

SNRdB = 10 log10 SNR

For a noise-less channel, SNR = infinity. Such a channel is not achievable.

Example: 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 ?

Prof. Mukesh N Tekwani [9869 488 356]

Page 8 of 10 Chap 3 – Data & Signals

In the above diagrams we have shown the case of a high SNR and low SNR

Distinguish between baseband transmission and broadband transmission.

Digital signals can be transmitted by one of the two ways: baseband transmission and

broadband transmission.

Baseband Transmission:

1. In baseband transmission we send a digital signal without changing it into an analog

signal.

2. For baseband transmission we require a low-pass channel. A low-pass channel is one

which has a bandwidth that starts from 0.

3. We require a dedicated medium with a bandwidth consisting of only one channel. E.g.,

the entire bandwidth of a cable connecting two computers is one single channel.

4. A low-pass channel with infinite bandwidth is ideal but such a medium cannot be realise

din practice. Below we show two low pass channels, one with a narrow bandwidth and

the other with a wide bandwidth.

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Chap 1 – Introduction Page 9 of 10

Low-pass Channel with wide Bandwidth:

1. If we want to preserve the exact form of a non-periodic digital signal we must send the

entire spectrum with the continuous range of frequencies between 0 and infinity.

2. This is possible only if we have a dedictaed medium of infinite bandwidth, between the

sender and the receiver. This medium should preserve the exact amlitude of each

component of the composite signal. But it is observed that the amplitudes of frequencies

near the end of the bandwidth are so small that they can be ignored.

3. We observe that the output signal is not an exact replica of the input signal and that the

data can be deduced from the received signal.

4. Thus, baseband transmission of a digital signal that preserves the shape of the digital

signal. This is possible only if we have a low-pass channel with infinite or very wide

bandwidth.

5. An example of a dedicated channel where the entire bandwidth of the medium is used as

one single channel is the LAN cable. E.g., in bus topology, only two stations can

communicate with each other at any given time.

6. If more than one transmission must be sent over a single channel, it must be done using

the technique of multiplexing.

Low-pass Channel with limited Bandwidth:

1. In a low pass chaneel with limited bandwidth, we approximate the digital signal with an

analog signal.The level of approximation dpends on the available bandwidth.

2. He required bandwidth is proportional to the bit rate. To increase the bit rate we must

have a higher bandwidth.

Broadband Transmission

1. In broadband transmission, the digital signal is changed into an analog signal for

transmission.

2. If the available channel is a bandpass channel, we cannot send a digital signal directly

through this channel. The digital signal must be converted to analog before transmission.

3. We use a bandpass channel for this purpose. A bandpass channel is one whose bandwidth

doesnot start from 0. Thus we can consider a low pass channel as a band pass channel

with the lower frequency starting at 0.

Prof. Mukesh N Tekwani [9869 488 356]

Page 10 of 10 Chap 3 – Data & Signals

In the figure below we show the modulation of a digital signal.

4. A digital signal is converted into a composite analog signal. We have used a single

frequency analog signal called a carrier. The amplitude of the carrier has been changed to

look like the digital signal. The result is a composite signal.

5. At the receiver end the composite signal is converted to digital and the result is the digital

signal that was originally transmitted.

6. Example of broadband transmission: sending digital data from a computer, throught the

telephone line. The converter used in this case is called a modem

(modulator/demodulator).