Analog transmission of digital data (Data Communications and Networking)

Telephone networks were originally built for human speech rather than for data. They were designed to transmit the electrical representation of sound waves, rather than the binary data used by computers. There are many occasions when data need to be transmitted over a voice communications network. Many people working at home still use a modem over their telephone line to connect to the Internet.

The telephone system (commonly called POTS for plain old telephone service) enables voice communication between any two telephones within its network. The telephone converts the sound waves produced by the human voice at the sending end into electrical signals for the telephone network. These electrical signals travel through the network until they reach the other telephone and are converted back into sound waves.

Analog transmission occurs when the signal sent over the transmission media continuously varies from one state to another in a wavelike pattern much like the human voice. Modems translate the digital binary data produced by computers into the analog signals required by voice transmission circuits. One modem is used by the transmitter to produce the analog signals and a second by the receiver to translate the analog signals back into digital signals.

The sound waves transmitted through the voice circuit have three important characteristics (see Figure 3.19). The first is the height of the wave, called amplitude. Amplitude is measured in decibels (dB). Our ears detect amplitude as the loudness or volume of sound. Every sound wave has two parts, half above the zero amplitude point (i.e., positive) and half below (i.e., negative), and both halves are always the same height.

The second characteristic is the length of the wave, usually expressed as the number of waves per second, or frequency. Frequency is expressed in hertz (Hz).4 Our ears detect frequency as the pitch of the sound. Frequency is the inverse of the length of the sound wave, so that a high frequency means that there are many short waves in a one-second interval, whereas a low frequency means that there are fewer (but longer) waves in 1 second.

The third characteristic is the phase, which refers to the direction in which the wave begins. Phase is measured in the number of degrees (°). The wave in Figure 3.19 starts up and to the right, which is defined as 0° phase wave. Waves can also start down and to the right (a 180° phase wave), and in virtually any other part of the sound wave.


When we transmit data through the telephone lines, we use the shape of the sound waves we transmit (in terms of amplitude, frequency, and phase) to represent different data values.

Sound wave

figure 3.19 Sound wave

Amplitude modulation

Figure 3.20 Amplitude modulation

We do this by transmitting a simple sound wave through the circuit (called the carrier wave) and then changing its shape in different ways to represent a 1 or a 0. Modulation is the technical term used to refer to these "shape changes." There are three fundamental modulation techniques: amplitude modulation, frequency modulation, and phase modulation. Once again, the sender and receiver have to agree on what symbols will be used (what amplitude, frequency, and phase will represent a 1 and a 0) and on the symbol rate (how many symbols will be sent per second).

Basic Modulation With amplitude modulation (AM) (also called amplitude shift keying [ASK]), the amplitude or height of the wave is changed. One amplitude is the symbol defined to be 0, and another amplitude is the symbol defined to be a 1. In the AM shown in Figure 3.20, the highest amplitude symbol (tallest wave) represents a binary 1 and the lowest amplitude symbol represents a binary 0. In this case, when the sending device wants to transmit a 1, it would send a high-amplitude wave (i.e., a loud signal). AM is more susceptible to noise (more errors) during transmission than is frequency modulation or phase modulation.

Frequency modulation (FM) (also called frequency shift keying [FSK]) is a modulation technique whereby each 0 or 1 is represented by a number of waves per second (i.e., a different frequency). In this case, the amplitude does not vary. One frequency (i.e., a certain number of waves per second) is the symbol defined to be a 1, and a different frequency (a different number of waves per second) is the symbol defined to be a 0. In Figure 3.21, the higher-frequency wave symbol (more waves per time period) equals a binary 1, and the lower frequency wave symbol equals a binary 0.

Frequency modulation

Figure 3.21 Frequency modulation

Phase modulation

Figure 3.22 Phase modulation

Phase modulation (PM) (also called phase shift keying [PSK]) is the most difficult to understand. Phase refers to the direction in which the wave begins. Until now, the waves we have shown start by moving up and to the right (this is called a 0° phase wave). Waves can also start down and to the right. This is called a phase of 180°. With phase modulation, one phase symbol is defined to be a 0 and the other phase symbol is defined to be a 1. Figure 3.22 shows the case where a phase of 0° symbol is defined to be a binary 0 and a phase of 180° symbol is defined to be a binary 1.

Sending Multiple Bits Simultaneously Each of the three basic modulation techniques (AM, FM, and PM) can be refined to send more than 1 bit at one time. For example, basic AM sends 1 bit per wave (or symbol) by defining two different amplitudes, one for a 1 and one for a 0. It is possible to send 2 bits on one wave or symbol by defining four different amplitudes. Figure 3.23 shows the case where the highest-amplitude wave is defined to be a symbol representing two bits, both 1′s. The next highest amplitude is the symbol defined to mean first a 1 and then a 0, and so on.

This technique could be further refined to send 3 bits at the same time by defining 8 different symbols, each with different amplitude levels or 4 bits by defining 16 symbols, each with different amplitude levels, and so on. At some point, however, it becomes very difficult to differentiate between the different amplitudes. The differences are so small that even a small amount of noise could destroy the signal.

This same approach can be used for FM and PM. Two bits could be sent on the same symbol by defining four different frequencies, one for 11, one for 10, and so on, or by defining four phases (0°, 90°, 180°, and 270°).

Two-bit amplitude modulation

Figure 3.23 Two-bit amplitude modulation 

Three bits could be sent by defining symbols with eight frequencies or eight phases (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). These techniques are also subject to the same limitations as AM; as the number of different frequencies or phases becomes larger, it becomes difficult to differentiate among them.

It is also possible to combine modulation techniques—that is, to use AM, FM, and PM techniques on the same circuit. For example, we could combine AM with four defined amplitudes (capable of sending 2 bits) with FM with four defined frequencies (capable of sending 2 bits) to enable us to send 4 bits on the same symbol.

One popular technique is quadrature amplitude modulation (QAM). QAM involves splitting the symbol into eight different phases (3 bits) and two different amplitudes (1 bit), for a total of 16 different possible values. Thus, one symbol in QAM can represent 4 bits. A newer version of QAM called 64-QAM sends 6 bits per symbol and is used in wireless LANs.

Bit Rate versus Baud Rate versus Symbol Rate The terms bit rate (i.e., the number bits per second transmitted) and baud rate are used incorrectly much of the time. They often are used interchangeably, but they are not the same. In reality, the network designer or network user is interested in bits per second because it is the bits that are assembled into characters, characters into words and, thus, business information.

A bit is a unit of information. A baud is a unit of signaling speed used to indicate the number of times per second the signal on the communication circuit changes. Because of the confusion over the term baud rate among the general public, ITU-T now recommends the term baud rate be replaced by the term symbol rate. The bit rate and the symbol rate (or baud rate) are the same only when one bit is sent on each symbol. For example, if we use AM with two amplitudes, we send one bit on one symbol. Here, the bit rate equals the symbol rate. However, if we use QAM, we can send 4 bits on every symbol; the bit rate would be four times the symbol rate. If we used 64-QAM, the bit rate would be six times the symbol rate. Virtually all of today’s modems send multiple bits per symbol.

Capacity of a Circuit

The data capacity of a circuit is the fastest rate at which you can send your data over the circuit in terms of the number of bits per second. The data rate (or bit rate) is calculated by multiplying the number of bits sent on each symbol by the maximum symbol rate. As we discussed in the previous section, the number of bits per symbol depends on the modulation technique (e.g., QAM sends 4 bits per symbol).

The maximum symbol rate in any circuit depends on the bandwidth available and the signal-to-noise ratio (the strength of the signal compared with the amount of noise in the circuit). The bandwidth is the difference between the highest and the lowest frequencies in a band or set of frequencies. The range of human hearing is between 20 Hz and 14,000 Hz, so its bandwidth is 13,880 Hz. The maximum symbol rate for analog transmission is usually the same as the bandwidth as measured in Hertz. If the circuit is very noisy, the maximum symbol rate may fall as low as 50 percent of the bandwidth. If the circuit has very little noise, it is possible to transmit at rates up to the bandwidth.

Digital transmission symbol rates can reach as high as two times the bandwidth for techniques that have only one voltage change per symbol (e.g., NRZ). For digital techniques that have two voltage changes per symbol (e.g., RZ, Manchester), the maximum symbol rate is the same as the bandwidth.

Standard telephone lines provide a bandwidth of 4,000 Hz. Under perfect circumstances, the maximum symbol rate is therefore about 4,000 symbols per second. If we were to use basic AM (1 bit per symbol), the maximum data rate would be 4,000 bits per second (bps). If we were to use QAM (4 bits per symbol), the maximum data rate would be 4 bits per symbol x 4,000 symbols per second = 16,000 bps. A circuit with a 10 MHz bandwidth using 64-QAM could provide up to 60 Mbps.

How Modems Transmit Data

The modem (an acronym for modulator/cferoodulator) takes the digital data from a computer in the form of electrical pulses and converts them into the analog signal that is needed for transmission over an analog voice-grade circuit. There are many different types of modems available today from dial-up modems to cable modems. For data to be transmitted between two computers using modems, both need to use the same type of modem. Fortunately, several standards exist for modems, and any modem that conforms to a standard can communicate with any other modem that conforms to the same standard.

A modem’s data transmission rate is the primary factor that determines the throughput rate of data, but it is not the only factor. Data compression can increase throughput of data over a communication link by literally compressing the data. V.44, the ISO standard for data compression, uses Lempel-Ziv encoding. As a message is being transmitted, Lempel-Ziv encoding builds a dictionary of two-, three-, and four-character combinations that occur in the message. Anytime the same character pattern reoccurs in the message, the index to the dictionary entry is transmitted rather than sending the actual data. The reduction provided by V.44 compression depends on the actual data sent but usually averages about 6:1 (i.e., almost six times as much data can be sent per second using V.44 as without it).

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