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UNIT - 1
Signals
SYLLABUS: Analog and digital data, Analog and digital signals; PERIODIC AND APERIODIC
SIGNALS, ANALOG SIGNALS: Simple analog signals; TIME AND FREQUENCY DOMAINS;
COMPOSITE SIGNALS: Frequency
spectrum
and
Bandwidth;
DIGTAL
SIGNALS:
Decomposition
of
digital
signal; TRANSMISSION MODES: Serial and Parallel
transmission/Asynchronous and Synchronous Transmission, Simplex, Half-Duplex and Full-Duplex
communication.
UNIT 1: Signals
CONTENTS:
Analog and digital data, Analog and digital signals; PERIODIC AND APERIODIC SIGNALS,
ANALOG SIGNALS: Simple analog signals; TIME AND FREQUENCY DOMAINS; COMPOSITE
SIGNALS: Frequency spectrum and Bandwidth; DIGTAL SIGNALS: Decomposition of
digital
signal; TRANSMISSION MODES: Serial and Parallel transmission/Asynchronous and
Synchronous Transmission, Simplex, Half-Duplex and Full-Duplex communication.
// ANALOG AND DIGITAL DATA : Data can he analog or digital. The analog data refers to
information that is continuous; digital data refers to information that has discrete states. For
example, an analog clock that has hour, minute, and second hands gives information in a continuous
form; the movements of the hands are continuous- On the other hand, a digital clock that reports the
hours and the minutes will change suddenly from 8:05 to 8:06.//
//ANALOG AND DIGITAL SIGNALS Like the data, signals can be either analog or digital. An
analog signal has infinitely many levels of intensity over a period of time. As the wave moves from
value A to value B, it passes through and includes an infinite number of values along its path. A
digital signal, on the other hand, can have only a limited number of defined values. Although each
value can be any number, it is often as simple as 1 and 0.//
//Periodic and Non periodic Signals
Both analog and digital signals can be of two forms; periodic or non periodic. A periodic signal
which repeats itself after fixed time period. The completion of one fall pattern is called a cycle.
Non periodic signal which does not repeats itself after fixed itself .In data communications, we
commonly use periodic analog signals (because they need less bandwidth) and non-periodic digital
signals (because they can represent variation in data)//
ANALOG SIGNALS
SIMPLE PERIODIC ANALOG SIGNALS
A simple periodic analog signal cannot be decomposed into simpler signals. e.g. Sine wave. The sine
wave is the most fundamental form of a periodic analog signal. Each cycle consists of a single arc
above the time axis followed by a single arc below it.
A sine wave can be represented by three parameters; the peak amplitude, the frequency, and the phase.
These three parameters fully describe a sine wave.
Peak Amplitude
The peak amplitude of a signal is the absolute value (A real number regardless of its sign) of its
highest intensity. For electric signals, peak amplitude is normally measured in volts.
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UNIT 1: Signals
Period and Frequency
Period is the amount of time, in seconds, which a signal needs to complete 1 cycle. Whereas
Frequency is the number of periods in 1 sec. The period and frequency are just one characteristic
defined in two ways. Period is the inverse of frequency, and vice-versa, as the following formulas
show.
1
1
𝑓= &
𝑡=
𝑡
𝑓
Period is formally expressed in seconds. Frequency is formally expressed in Hertz (Hz), which is
cycle per second.
Time and Frequency Domains
Fig: sine wave in time domain
Fig: sine wave in frequency domain
The time-domain plot shows changes in signal amplitude with respect to time. Phase is not
shown on a time-domain plot.
A frequency-domain plot is concerned with only the peak value and the frequency. Changes of
amplitude during one period are not shown. Above figures show a sine wave in both the time and
frequency domains.
COMPOSITE SIGNALS
A composite signal is made up of many simple sine waves with different frequencies, amplitudes and
phases. It can be periodic or non-periodic. A periodic composite signal can be decomposed into a
series of simple sine waves with discrete frequencies. A non-periodic composite signal can be
decomposed into a combination of an infinite number of simple sine waves with continuous
frequencies, frequencies that have real values.
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UNIT 1: Signals
Above figure shows a composite periodic signal with frequency f. It can be decomposed in time and
frequency domain as follows:
The amplitude of the sine wave with frequency f is almost the same as the peak amplitude of the
composite signal. The amplitude of the sine wave with frequency 3f is one-third of that of the first,
and the amplitude of the sine wave with frequency 9f is one-ninth of the first.
The frequency of the sine wave with frequency f is the same as the frequency of the composite
signal; it is called the fundamental frequency, or first harmonic. The sine wave with frequency
3fhas a frequency of 3 times the fundamental frequency; it is called the third harmonic. The third sine
wave with frequency 9f has a frequency of 9 times the fundamental frequency; it is called the ninth
harmonic.
The decomposition of the signal in frequency domain is discrete; it has frequencies f, 3f and 9f.
Because f is an integral number, 3f and 9fare also integral numbers. There are no frequencies such as
1.2for2.6f. The frequency domain of the periodic composite signal is always made of discrete spikes.
Above figure shows a composite non-periodic signal. As there is infinite number of simple sine
frequencies, there decomposition in time domain is not possible. Although the number of frequencies
is infinite, the range is limited. Therefore the decomposition of signal in frequency domain will result
in a continuous curve. In the following figure height of vertical line is the amplitude of corresponding
frequency.
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UNIT 1: Signals
[Important]BANDWIDTH
The range of frequencies contained in a composite signal is its bandwidth. The bandwidth is
normally a difference between two numbers. For example, if a composite signal contains frequencies
between 1000 and 5000, its bandwidth is 5000 - 1000, or 4000.
The bandwidth of the periodic signal contains all integer frequencies between 1000 and 5000 (1000,
1001, 1002...).
Fig: Bandwidth of periodic composite signal
Fig: Bandwidth of non-periodic composite signal
The bandwidth of the non-periodic signals has the same range, but the frequencies are continuous.
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 maximum
amplitude of 10 V. [3m]
Solution:Let fh be the highest frequency, fl be the lowest frequency, and B the bandwidth. Then
𝐵 = 𝑓ℎ − 𝑓𝑙 = 900 − 100 = 800 𝐻𝑧
The spectrum has only five spikes at 100, 300, 500, 700 & 900 Hz.
What is the bandwidth of a signal that can be decomposed into five sine waves with frequencies at
0, 30, 40, 120 and 300 Hz ? All peak amplitudes are the same. Draw the bandwidth. 3
Hint: 𝐵 = 𝑓ℎ − 𝑓𝑙 = 300 − 0 = 300 𝐻𝑧& figure is same as previous one.
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 be the lowest frequency, and B the bandwidth. Then
𝐵 = 𝑓ℎ − 𝑓𝑙 → 20 = 60 − 𝑓𝑙 → 𝑓𝑙 = 60 − 20 = 40𝐻𝑧
The spectrum contains all the integer frequencies.
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UNIT 1: Signals
A non-periodic 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 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. Following figure shows the frequency domain and the bandwidth.
DIGITAL SIGNALS
A digital signal is defined as the signal which has only finite numbers of distinct values. For example,
1 can be encoded as a positive voltage and a 0 as zero voltage. A digital signal can have more than
two levels. In this case, we can send more than 1 bit for each level. Following figure shows two
signals, one with two levels and the other with four.
Similarly if there are eight levels then each signal level will represent three bits.
This can be calculated as:
No. of bits per level = log 2 n
Where n is the no. of levels.
Bit Rate: bit rate = bits Per Sample * samples Per Second * channel
It is the no. of bits sent in one second. It is expressed in bps. For an example, if we need to download a text file
at a rate of 100 pages per minute. If the page consists of 24 lines and each line has 80 characters. Let each
character requires 8 bits, then the bit rate can be calculated as,
100 × 24 × 80 × 8 = 16,36,000 𝑏𝑝𝑠 = 1.636 𝑀𝑏𝑝𝑠
A digitized voice channel is made by digitizing a 4 KHz bandwidth analog voice signal. We need to
sample the signal at twice the highest frequency. We assume that each sample requires 8 bits. What
is required bit rate?
Solution
This can be calculated as 2 × 4000 × 8 = 64,000 bps = 64Kbps
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UNIT 1: Signals
What is the bit rate for high-definition TV (HDTV)?
Solution
HDTV uses digital signals to broadcast high quality video signals. The HDTV screen is normally a
ratio of 16: 9 (in contrast to 4: 3 for regular TV), which means the screen is wider. There are 1920 by
1080 pixels per screen, and the screen is renewed 30 times per second. Twenty-four bits represents
one color pixel. We can calculate the bit rate as
1920 x 1080 x 30 x 24 = 1,492,992,000 or 1.5 Gbps
Bit Length
The bit length is the distance one bit occupies on the transmission medium.
Bit length = propagation speed x bit duration
.
TRANSMISSION MODES
The transmission of data from one device to another can take place in either parallel or serial mode. In
parallel mode, multiple bits are sent with each clock pulse. In serial mode, 1 bit is sent with each
clock pulse. Serial transmission can be classified into three modes : asynchronous, synchronous, and
isochronous.
Parallel Transmission
In the parallel transmission, binary data, consisting of 1s and 0s, are organized into groups of
n bits each. By grouping, we can send data n bits at a time instead of single bit. This requires n wires
to send n bits at one time. Following figure shows working of parallel transmission for n=8.
The advantage of parallel transmission is that it can increase the transfer speed by a factor of n over
serial transmission.
But the disadvantage of Parallel transmission is that it requires n communication lines (wires in the
example) just to transmit the data stream. Because of this drawback it is usually limited to short
distances.
Serial Transmission
In serial transmission one bit follows another, so it requires only one communication channel rather
than n to transmit data between two communicating devices. Following figure shows working of
serial transmission.
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UNIT 1: Signals
The advantage of serial transmission is that it reduces the cost of transmission over parallel by factor
of n.
But the disadvantage of serial transmission is that the transfer speed falls by a factor of n over parallel
transmission.
Synchronous vs. Asynchronous
 Synchronous data transfer: sender and receiver use the same clock signal
o supports high data transfer rate
o needs clock signal between the sender and the receiver
o requires master/slave configuration
 Asynchronous data transfer: sender provides a synchronization signal to the
receiver before starting the transfer of each message
o does not need clock signal between the sender and the receiver
o slower data transfer rate
There are many serial data transfer protocols. The protocols for serial data transfer can be
grouped into two types: synchronous and asynchronous. For synchronous data transfer, both
the sender and receiver access the data according to the same clock. Therefore, a special line
for the clock signal is required. A master (or one of the senders) should provide the clock
signal to all the receivers in the synchronous data transfer.
Asynchronous Transmission
For asynchronous data transfer, there is no common clock signal between the sender
and receivers. Therefore, the sender and the receiver first need to agree on a data transfer
speed. This speed usually does not change after the data transfer starts.
Asynchronous transmission sends only one character at a time where a character is either a
letter of the alphabet or number or control character i.e. it sends one byte of data at a time.
• Bit synchronization between two devices is made possible using start bit and stop bit.
• Start bit indicates the beginning of data i.e. alerts the receiver to the arrival of new group of
bits. A start bit usually 0 is added to the beginning of each byte.
• Stop bit indicates the end of data i.e. to let the receiver know that byte is finished, one or
more additional bits are appended to the end of the byte. These bits, usually 1s are called stop
bits.
Addition of start and stop increase the number of data bits. Hence more bandwidth is
consumed in asynchronous transmission.
• There is idle time between the transmissions of different data bytes. This idle time is also
known as Gap
• The gap or idle time can be of varying intervals. This mechanism is called Asynchronous,
because at byte level sender and receiver need not to be synchronized. But within each byte,
receiver must be synchronized with the incoming bit stream.
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UNIT 1: Signals
Application of Asynchronous Transmission
1. Asynchronous transmission is well suited for keyboard type-terminals and paper tape
devices. The advantage of this method is that it does not require any local storage at the
terminal or the computer as transmission takes place character by character.
2. Asynchronous transmission is best suited to Internet traffic in which information is
transmitted in short bursts. This type of transmission is used by modems.
Advantages of Asynchronous transmission
1. This method of data transmission is cheaper in cost as compared to synchronous e.g. If
lines are short, asynchronous transmission is better, because line cost would be low and idle
time will not be expensive.
2. In this approach each individual character is complete in itself, therefore if character is
corrupted during transmission, its successor and predecessor character will not be affected.
3. It is possible to transmit signals from sources having different bit rates.
4. The transmission can start as soon as data byte to be transmitted becomes available.
5. Moreover, this mode of data transmission in easy to implement.
Disadvantages of asynchronous transmission
1. This method is less efficient and slower than synchronous transmission due to the overhead
of extra bits and insertion of gaps into bit stream.
2. Successful transmission inevitably depends on the recognition of the start bits. These bits
can be missed or corrupted.
Synchronous Transmission
Synchronous transmission does not use start and stop bits.
• In this method bit stream is combined into longer frames that may contain multiple bytes.
• There is no gap between the various bytes in the data stream.
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UNIT 1: Signals
In the absence of start & stop bits, bit synchronization is established between sender
&receiver by 'timing' the transmission of each bit.
• Since the various bytes are placed on the link without any gap, it is the responsibility of
receiver to separate the bit stream into bytes so as to reconstruct the original information.
• In order to receive the data error free, the receiver and sender operates at the same clock
frequency.
Application of Synchronous transmission
• Synchronous transmission is used for high speed communication between computers.
Advantage of Synchronous transmission
1. This method is faster as compared to asynchronous as there are no extra bits (start bit &
stop bit) and also there is no gap between the individual data bytes.
Disadvantages of Synchronous transmission
1. It is costly as compared to asynchronous method. It requires local buffer storage at the two
ends of line to assemble blocks and it also requires accurately synchronized clocks at both
ends. This lead to increase in the cost.
2. The sender and receiver have to operate at the same clock frequency. This requires proper
synchronization which makes the system complicated.
Comparison between Serial and Parallel transmission
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UNIT 1: Signals
Comparison between Asynchronous and Synchronous.
Isochronous
In real-time audio and video, in which uneven delays between frames are not acceptable, synchronous
transmission cannot work. For example, TV images are broadcast at the rate of 30 images per second;
they must be viewed at the same rate. If each image is sent by using one or more frames, there should
be no delays between frames. For this type of application, synchronization between characters is not
enough; the entire stream of bits must be synchronized. Such type of synchronization can be achieved
in isochronous transmission.
Type of Communication Systems
The communication system can be classified into three categories
1. Simplex
2. Full Duplex
3. Half Duplex
Simplex
A simplex system is communication systems in which the message can be send in one direction only.
Radio and TV broadcasting are e.g.
User – Transmitter – Receiver – User
Full Duplex
A full duplex system is one in which the link is capable of transmitting in both the direction, at the
same.
E.g.: telephone system.
Half Duplex
In a half-duplex system, each end may transmit, but only one at a time. This requires both transmitting
and receiving circuitry at each end, but the actual link between the two ends may be shared.
e.g.: A citizen’s band radio where a frequency channel is shared and each party has to say “over” to
switch the direction of the communication.
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UNIT 1: Signals
QUESTIONS
1. What is the bandwidth of a signal that can be decomposed into five sine waves with
frequencies at 0, 30, 40, 120 and 300 Hz? All peak amplitudes are the same. Draw the
bandwidth.
2. Suppose that a digitized TV picture is to be transmitted from a source that uses a matrix
of 480 x 500 picture elements (pixels), where each pixel can take on one of 32 intensity
valves. Assume that 30 pictures are sent per second. Find the source rate R in bps.
3. Since parallel communications transmit bits simultaneously, why not design parallel
communications with an arbitrarily large number of parallel lines to decrease
transmission time?
4. Distinguish among simplex, half duplex, and full-duplex communication.
What is the bit rate for the signal in figure?
1.
2. A non-periodic composite signal contains frequencies from 10 to 40 KHz. The peak
amplitude is 12 volt for the lowest and the highest signals and is 30 volt for the 20 KHz
signal. Assuming that the amplitudes change gradually from the minimum to the
maximum, draw the frequency spectrum.
3. Why do asynchronous communications require additional start and stop bits? What is
wrong with letting the first bit in a transmission acts as a start bit and the last one acts
as a stop bit?
5.
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