2. Modulation techniques

1.1.13 Shannon's theory

Manchester differential encoding example.

1.1.14 Sampling theory

at 44:1 kHz.

8

as follows:

Figure 5.

Shannon studied noisy channels, and his theory is based upon the fact that

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

successfully distinguished. This influences the maximum bit rate that can be used

To increase the data rate, a channel with high S/N should be used. Other means

To convert a continuous signal x(t) into a digital form [8], it is first sampled at equal intervals of time. To be able to reconstruct a sampled signal, xδð Þt is defined as

The sampling interval Ts is 1/fs, where the sampling frequency fs should be at least twice the highest frequency component fmax of the original signal x(t). The

An analogue signal with a given frequency f<sup>1</sup> can be converted into a digital

the form of pulses with different amplitudes called pulse amplitude modulation (PAM). The PAM signal is then quantised, and every level is given a binary code number. This process is called pulse-code modulation (PCM). The sampling frequency fs has to be at least twice as much as the signal frequency being sampled f <sup>1</sup> in order to produce a good approximation of the original signal that can be reproduced and converted back to analogue form. In telephony systems the 8-kHz frequency is used to sample voice that is encoded using 8-bit code. The bit rate in this case is 8000 � 8 ¼ 64 kbps. In compact disc (CD) technology, the audio is sampled

Data rate in bps ¼ bandwidth � log2ð Þ 1 þ S=N (1)

x nT ð Þ<sup>s</sup> δð Þ t � nTs (2)

. A sampled signal has

a signal has to have high signal-to-noise (S/N) ratio in order to be

xδðÞ¼ t ∑

form by sampling it at a constant frequency fs, where f <sup>1</sup> , fs

∞ n¼�∞

that can increase the bit rate is data compression.

frequency 2fmax is called the Nyquist frequency.

1.1.15 Analogue-to-digital (A/D) conversion

In the past, digital networks were connected through telephone networks via the modem (modulation/demodulation). Modern telecommunications systems utilise optical fibres that carry many digital channels, which can be translated into voice signals in a telephone by using a codec (coder/decoder). This involves digital-toanalogue (D/A) and analogue-to-digital (A/D) conversions. When a signal m tðÞ¼ Am cos <sup>2</sup>π<sup>f</sup> <sup>m</sup><sup>t</sup> <sup>þ</sup> <sup>ϕ</sup>mð Þ<sup>t</sup> is transmitted, it is normally modulated using a carrier c tðÞ¼ Ac sin <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> <sup>þ</sup> <sup>ϕ</sup>cð Þ<sup>t</sup> signal, which can be changed or modulated in amplitude (Ac), phase shift (ϕc) or frequency (fc) [9]. The carrier signal can be generalised as c tðÞ¼ Acð Þ<sup>t</sup> sin <sup>2</sup>πfct <sup>þ</sup> <sup>ϕ</sup>cð Þ<sup>t</sup> .

## 2.1 Analogue modulation

To transmit analogue signals over long distances, analogue modulation techniques are used by changing either the amplitude, phase or frequency of analogue signals.

### 2.1.1 Amplitude modulation (AM)

Amplitude modulation (AM) takes place when Acð Þt is linearly related to the modulating signals (message). In this modulation technique, the carrier frequency is kept constant, and its amplitude is varied according to the amplitude of the transmitted analogue signal as shown in Figure 6. An AM signal y tð Þ is the result of multiplying the message m tð Þ and carrier c tð Þ functions. Assuming a sinusoidal carrier signal defined as c tðÞ¼ Ac sin <sup>2</sup>πfct is used to modulate the message signal m tðÞ¼ Am cos <sup>2</sup>π<sup>f</sup> <sup>m</sup><sup>t</sup> <sup>þ</sup> <sup>ϕ</sup>ð Þ<sup>t</sup> :

$$\begin{aligned} y(t) &= [\mathbf{1} + m(t)/A\_c]c(t) \\ y(t) &= [\mathbf{1} + \mathbf{m}\cos\left(2\pi f\_m t + \phi\right)]A\_c \sin\left(2\pi f\_c t\right) \end{aligned} \tag{3}$$

In the above equation, m is the modulation index, which is the ratio of the amplitude of the message signal Am to the amplitude Ac of the carrier signal.

y tðÞ¼ Ac cos 2πf <sup>c</sup>t þ

describes the variation in carrier frequency compared [10]:

terms of the phase modulation index mp as ϕðÞ¼ t mpm tð Þ.

much greater than 1 (for wideband FM).

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2.1.3 Phase modulation (PM)

2.2 Digital modulation

Figure 7. FM modulation.

11

Amf <sup>Δ</sup> f m

In the above equation, Am is the amplitude of the message signal, f <sup>m</sup> is the frequency of the message signal and f <sup>Δ</sup> is the maximum frequency that corresponds

> mf <sup>¼</sup> <sup>f</sup> <sup>Δ</sup> f m

The frequency modulation index can be less than 1 (for narrowband FM) or

Phase modulation (PM) takes place when ϕð Þt is linearly related to the modulating signal. In this modulation technique, the amplitude of the carrier signal is kept constant, and its phase is varied according to the amplitude of the transmitted analogue signal as shown in Figure 8. The phase of the PM signal can be written in

Transmission of digital signals involves modulation of amplitude, frequency or phase of carrier signals. The difference between analogue and digital modulation is that in digital modulation, the changes are at discrete intervals. For example, the

to the maximum amplitude Am value. The frequency modulation index mf

sin <sup>2</sup>π<sup>f</sup> <sup>m</sup><sup>t</sup> (5)

(6)

Figure 6. AM modulation.

To be able to recover the message, m should be less than 1, i.e., 1 , m . 0. The resulting product function y tð Þ is composed of three frequencies:

$$y(t) = A\_c \sin\left(2\pi f\_c t\right) + \frac{1}{2} \mathbf{m} A\_c \left[\sin\left(2\pi \left[f\_c + f\_m\right]t + \phi\right) + \sin\left(2\pi \left[f\_c - f\_m\right]t - \phi\right)\right] \tag{4}$$

The equation above shows three frequencies:


#### 2.1.2 Frequency modulation (FM)

Frequency modulation (FM) takes place when the time derivative of ϕð Þt is linearly related to the modulating signal. In this modulation technique, the amplitude of the carrier signal is kept constant, and its frequency is varied according to the amplitude of the transmitted analogue signal as shown in Figure 7. Frequency and phase modulations are considered as special cases of angle modulation s tðÞ¼ Ac cos <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> <sup>þ</sup> <sup>ϕ</sup>ð Þ<sup>t</sup> . The carrier frequency is changed such that the frequency fc depends on the message signal. Since the frequency is the derivative of the phase, the relation between the input signal and frequency can be written as [9] ϕ0 ðÞ¼ t mfm tð Þ. The FM signal y tð Þ can be written as

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$$y(t) = A\_c \left[ \cos \left( 2\pi f\_c t + \frac{A\_m f\_{\Delta}}{f\_m} \sin \left( 2\pi f\_m t \right) \right) \right] \tag{5}$$

In the above equation, Am is the amplitude of the message signal, f <sup>m</sup> is the frequency of the message signal and f <sup>Δ</sup> is the maximum frequency that corresponds to the maximum amplitude Am value. The frequency modulation index mf describes the variation in carrier frequency compared [10]:

$$\mathbf{m\_{f}} = \frac{f\_{\Delta}}{f\_{m}} \tag{6}$$

The frequency modulation index can be less than 1 (for narrowband FM) or much greater than 1 (for wideband FM).

#### 2.1.3 Phase modulation (PM)

Phase modulation (PM) takes place when ϕð Þt is linearly related to the modulating signal. In this modulation technique, the amplitude of the carrier signal is kept constant, and its phase is varied according to the amplitude of the transmitted analogue signal as shown in Figure 8. The phase of the PM signal can be written in terms of the phase modulation index mp as ϕðÞ¼ t mpm tð Þ.

#### 2.2 Digital modulation

To be able to recover the message, m should be less than 1, i.e., 1 , m . 0. The

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2. The sum of the carrier and modulated frequencies f <sup>c</sup> þ f <sup>m</sup> þ ϕ with the same

3. The difference between the carrier and modulated frequencies f <sup>c</sup> � f <sup>m</sup> � ϕ

Frequency modulation (FM) takes place when the time derivative of ϕð Þt is linearly related to the modulating signal. In this modulation technique, the amplitude of the carrier signal is kept constant, and its frequency is varied according to the amplitude of the transmitted analogue signal as shown in Figure 7. Frequency and phase modulations are considered as special cases of angle modulation s tðÞ¼ Ac cos <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> <sup>þ</sup> <sup>ϕ</sup>ð Þ<sup>t</sup> . The carrier frequency is changed such that the frequency fc depends on the message signal. Since the frequency is the derivative of the phase, the relation between the input signal and frequency can be written as [9]

 <sup>t</sup> <sup>þ</sup> <sup>ϕ</sup> <sup>þ</sup> sin <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> � <sup>f</sup> <sup>m</sup> <sup>t</sup> � <sup>ϕ</sup>

(4)

mAc sin 2π fc þ f <sup>m</sup>

resulting product function y tð Þ is composed of three frequencies:

1 2

The equation above shows three frequencies:

with the negative phase shift of the message signal.

ðÞ¼ t mfm tð Þ. The FM signal y tð Þ can be written as

y tðÞ¼ Ac sin <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> <sup>þ</sup>

Figure 6. AM modulation.

1. The carrier frequency fc.

2.1.2 Frequency modulation (FM)

ϕ0

10

phase shift of the message signal.

Transmission of digital signals involves modulation of amplitude, frequency or phase of carrier signals. The difference between analogue and digital modulation is that in digital modulation, the changes are at discrete intervals. For example, the

Figure 7. FM modulation.

Figure 8. PM modulation.

amplitude of the carrier signal can be assigned to a maximum value or zero to represent the binary data 1 and 0.

### 2.2.1 Frequency-shift keying (FSK)

Frequency-shift keying is called also frequency modulation (FM). A bit 0 corresponds to low frequency, and a 1 corresponds to high frequency as shown in Figure 9. An FSK signal s(t) can be written as

$$s(t) = \begin{cases} A\_\epsilon \cos\left(2\pi (f\_\epsilon + k)t\right), & \text{if } \begin{array}{l} bit = 1 \\ A\_\epsilon \cos\left(2\pi (f\_\epsilon - k)t\right), & \text{if } \begin{array}{l} bit = 0 \end{array} \end{array} \tag{7}$$

Figure 9. FSK modulation.

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Figure 10. ASK modulation.

13

In the equation above, k is a constant shift in frequency. Obviously, the FSK uses two frequencies ( f <sup>c</sup> þ k and f <sup>c</sup> � k) for logic 0 and 1, respectively. This type of FSK is called binary FSK (BFSK).

In case k and 3k are used to shift the carrier frequency, the resulting FSK signal has four different frequencies and can be utilised to encode the binary codes 00, 01, 10 and 11, as follows:

$$s(t) = \begin{cases} A\_\varepsilon \cos\left(2\pi (f\_c + 3k)t\right), & \text{if } \text{ bits} = 00\\ A\_\varepsilon \cos\left(2\pi (f\_c - k)t\right), & \text{if } \text{ bits} = 01\\ A\_\varepsilon \cos\left(2\pi (f\_c + k)t\right), & \text{if } \text{ bits} = 10\\ A\_\varepsilon \cos\left(2\pi (f\_c - 3k)t\right), & \text{if } \text{ bits} = 11 \end{cases} \tag{8}$$

#### 2.2.2 Amplitude-shift keying (ASK)

Amplitude-shift keying is similar to amplitude modulation (AM) as shown in Figure 10. Each signal amplitude is assigned to a sequence of bits. If four amplitudes Telecommunications Protocols Fundamentals DOI: http://dx.doi.org/10.5772/intechopen.86338

Figure 9. FSK modulation.

amplitude of the carrier signal can be assigned to a maximum value or zero to

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sponds to low frequency, and a 1 corresponds to high frequency as shown in

Frequency-shift keying is called also frequency modulation (FM). A bit 0 corre-

s tðÞ¼ Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> <sup>þ</sup> <sup>k</sup> � �<sup>t</sup> � �, if bit <sup>¼</sup> <sup>1</sup>

In the equation above, k is a constant shift in frequency. Obviously, the FSK uses two frequencies ( f <sup>c</sup> þ k and f <sup>c</sup> � k) for logic 0 and 1, respectively. This type of FSK

In case k and 3k are used to shift the carrier frequency, the resulting FSK signal

Amplitude-shift keying is similar to amplitude modulation (AM) as shown in Figure 10. Each signal amplitude is assigned to a sequence of bits. If four amplitudes

has four different frequencies and can be utilised to encode the binary codes

Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> � <sup>k</sup> � �<sup>t</sup> � �, if bit <sup>¼</sup> <sup>0</sup>

Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> <sup>þ</sup> <sup>3</sup><sup>k</sup> � �<sup>t</sup> � �, if bits <sup>¼</sup> <sup>00</sup> Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> � <sup>k</sup> � �<sup>t</sup> � �, if bits <sup>¼</sup> <sup>01</sup> Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> <sup>þ</sup> <sup>k</sup> � �<sup>t</sup> � �, if bits <sup>¼</sup> <sup>10</sup> Ac cos <sup>2</sup><sup>π</sup> <sup>f</sup> <sup>c</sup> � <sup>3</sup><sup>k</sup> � �<sup>t</sup> � �, if bits <sup>¼</sup> <sup>11</sup>

(7)

(8)

represent the binary data 1 and 0.

Figure 8. PM modulation.

2.2.1 Frequency-shift keying (FSK)

is called binary FSK (BFSK).

00, 01, 10 and 11, as follows:

Figure 9. An FSK signal s(t) can be written as

s tðÞ¼

2.2.2 Amplitude-shift keying (ASK)

12

8 >>><

>>>:

(

Figure 10. ASK modulation.

are considered, the following bit code sequences can be defined as 00, 01, 10 and 11. A ASK signal s(t) can be written as

$$s(t) = \begin{cases} A\_\epsilon \cos\left(2\pi f\_\epsilon t\right), & \text{if } \begin{array}{l} bit=1\\ \mathbf{0}, \end{array} \end{cases} \quad \text{if } \begin{array}{l} bit=\mathbf{1} \\ \mathbf{0} \end{array} \tag{9}$$

#### 2.2.3 Phase-shift keying (PSK)

Phase-shift keying (PSK) is also called phase modulation (PM). The signal can have a variable phase as shown in Figure 11. If the signal is compared with its predecessor, this technique is called differential phase-shift keying (DPSK). Each phase shift can be assigned to a given binary code [11]. A PSK signal s tð Þ can be written as

$$s(t) = \begin{cases} A\_\iota \cos\left(2\pi f\_\iota t + \pi\right), & \text{if } \operatorname{ bit} = 1\\ A\_\iota \cos\left(2\pi f\_\iota t\right) & \text{if } \operatorname{ bit} = 0 \end{cases} \tag{10}$$

Since the above equation contains two distinct phases, this type is called binary phase-shift keying (BPSK). If the number of phase variations is increased to 4, the quadrature PSK (QPSK) ca be defined as follows:

$$s(t) = \begin{cases} A\_c \cos\left(2\pi f\_c t + \frac{\pi}{4}\right), & \text{if} \quad bits = 00 \\\\ A\_c \cos\left(2\pi f\_c t + \frac{3\pi}{4}\right), & \text{if} \quad bits = 01 \\\\ A\_c \cos\left(2\pi f\_c t + \frac{5\pi}{4}\right), & \text{if} \quad bits = 10 \\\\ A\_c \cos\left(2\pi f\_c t + \frac{7\pi}{4}\right), & \text{if} \quad bits = 11 \end{cases} \tag{11}$$

• Pulse width modulation (PWM): In PWM as shown in Figure 13, the width of each pulse is related to the modulating signal. This type of modulation is used

• Pulse position modulation (PPM): In PPM as shown in Figure 14, the position

1. PCM: This modulation technique is achieved by sampling the message signal and assigning a digital code (quantisation) to each pulse. The level of the signal is not transmitted; instead the quantised code is assigned according to the available bits for encoding. For example, in 8-bit PCM (with n ¼ 8), each level is assigned to a discrete value between 0 and 255. For a signal that has a bandwidth (BW) and a sampling rate of 2BW, the number of transmitted

2. Delta modulation: In delta modulation, only the difference between the previous and following codes is sent, as shown in Figure 15. For a reference signal msð Þt and a message signal m tð Þ, the difference Δð Þt is computed and fed to a pulse generator in order to produce the delta-modulated signal to be

> þ∞ n¼�∞

δð Þ t � nTs (13)

y tðÞ¼ Δð Þt ∑

in DC motor control applications.

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2.2.6 Digital pulse modulation

Figure 11. PSK modulation.

pulses becomes 2nBW.

transmitted:

15

of each pulse is related to the modulating signal.

Digital pulse modulation includes two types:

#### 2.2.4 Quadrature amplitude modulation (QAM)

Though the above three approaches can be used with any number of signals, they tend to be difficult to implement due to the fact that special hardware will be needed to distinguish between adjacent amplitudes, phases and frequencies. To overcome this limitation, a combination of bits can be assigned to groups of signals that can be different in amplitude and phase, for example. For example, using signals with two amplitudes and two phase shifts produces four different signals.

#### 2.2.5 Analogue pulse modulation

Pulse modulation can be achieved by modifying either amplitude, width or position of a pulse signal:

• Pulse amplitude modulation (PAM): The PAM signal (as shown in Figure 12) is similar to the sampled signal. The pulses in PAM can have a finite width unlike the sampling delta pulses. The PAM-modulated signal y tð Þ can be written as

$$\gamma(t) = \sum\_{k=-\infty}^{+\infty} \varkappa(k)\delta(t-k) \tag{12}$$

Telecommunications Protocols Fundamentals DOI: http://dx.doi.org/10.5772/intechopen.86338

Figure 11. PSK modulation.

are considered, the following bit code sequences can be defined as 00, 01, 10 and 11.

Telecommunication Systems – Principles and Applications of Wireless-Optical Technologies

s tðÞ¼ Ac cos <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> � �, if bit <sup>¼</sup> <sup>1</sup>

�

assigned to a given binary code [11]. A PSK signal s tð Þ can be written as

Ac cos <sup>2</sup>πfct <sup>þ</sup> <sup>π</sup>

Ac cos 2πf <sup>c</sup>t þ

Ac cos 2πf <sup>c</sup>t þ

Ac cos 2πf <sup>c</sup>t þ

using signals with two amplitudes and two phase shifts produces four

y tðÞ¼ ∑ þ∞ k¼�∞

(

8

>>>>>>>>>>>><

>>>>>>>>>>>>:

quadrature PSK (QPSK) ca be defined as follows:

s tðÞ¼

2.2.4 Quadrature amplitude modulation (QAM)

different signals.

2.2.5 Analogue pulse modulation

position of a pulse signal:

written as

14

0, if bit ¼ 0

Phase-shift keying (PSK) is also called phase modulation (PM). The signal can have a variable phase as shown in Figure 11. If the signal is compared with its predecessor, this technique is called differential phase-shift keying (DPSK). Each phase shift can be

s tðÞ¼ Ac cos <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> <sup>þ</sup> <sup>π</sup> � �, if bit <sup>¼</sup> <sup>1</sup>

Since the above equation contains two distinct phases, this type is called binary phase-shift keying (BPSK). If the number of phase variations is increased to 4, the

> 4 � �

3π 4 � �

5π 4 � �

7π 4 � �

Though the above three approaches can be used with any number of signals, they tend to be difficult to implement due to the fact that special hardware will be needed to distinguish between adjacent amplitudes, phases and frequencies. To overcome this limitation, a combination of bits can be assigned to groups of signals that can be different in amplitude and phase, for example. For example,

Pulse modulation can be achieved by modifying either amplitude, width or

• Pulse amplitude modulation (PAM): The PAM signal (as shown in Figure 12) is similar to the sampled signal. The pulses in PAM can have a finite width unlike the sampling delta pulses. The PAM-modulated signal y tð Þ can be

, if bits ¼ 00

, if bits ¼ 01

, if bits ¼ 10

, if bits ¼ 11

x kð Þδð Þ t � k (12)

Ac cos <sup>2</sup>π<sup>f</sup> <sup>c</sup><sup>t</sup> � � if bit <sup>¼</sup> <sup>0</sup>

(9)

(10)

(11)

A ASK signal s(t) can be written as

2.2.3 Phase-shift keying (PSK)

