Modulation

Type of physical science: Modulation, Acoustics, Electromagnetism, Classical physics

Field of study: Acoustics

A modification of a time-varying signal, often in a way that permits it to convey information, is called "modulation." By modulating electromagnetic waves, it is possible to transmit sounds, images, and data as radio and television signals. By modulating audio-frequency sound waves, it is possible to transmit digital data over telephone lines. Modulation can also be used to modify the timbre and quality of musical sounds.

Overview

Modulation most often occurs when one wave, usually referred to as the "signal," modifies another, generally referred to as the "carrier." The signal contains the information that is to be transferred. The carrier is a wave of the correct type and frequency to efficiently travel through the medium involved. For example, sound waves generated by a person's mouth and vocal cords can be converted by a microphone into fluctuations in electric current that can then be used to modulate a radio frequency electromagnetic wave that is broadcast from an antenna. A radio, located at a considerable distance from the antenna, can intercept some of these waves, demodulate the signal to obtain an electric current that fluctuates in the audio frequencies, and then use this current to drive a speaker or earphone. Whenever one varying parameter alters another, modulation is occurring.

The concept of modulation can be understood by considering the records of a fictional lawn-care company located in the northern United States. Imagine that this company always mows the grass when it is three inches long, bills its customers after each mowing, and makes deposits into its bank account every Friday. The bank records of this company would show that deposits were made every seven days, that is, at a constant frequency. The size of the deposits would vary with growing conditions. They would be greatest during periods of fast lawn growth in late spring and early fall, moderate during the summer, and very small during the winter months. The amplitude of the periodic event (the size of the bank deposit) is being modulated by the season. If the data covering four years were graphed, there would be 208 deposits, four major lows (one each winter), four minor dips (summers), and eight highs (springs and falls).

An examination of the company's time sheets would reveal that each visit to a particular home had the same duration (the size of the lawn stays the same), corresponding to a constant amplitude. During times of rapid growth, however, visits are made at shorter intervals, that is, with greater frequency. Therefore the frequency is being modulated by the seasons. The number of visits per month over a four-year period would show four major lows (one each winter), four minor dips, and eight highs.

Information about lawn growth can be derived from either series of data, because the variations in growth rate occur at a much slower rate than the recurring bank deposits or mowing visits. Note, too, that in order to infer much about growth rate, it is necessary to have a fairly complete record.

In general terms, the seasonal fluctuations can be considered to be the "signal" and the recurring events to be the "carriers." These two cases demonstrate amplitude modulation (AM) and frequency modulation (FM), two familiar ways in which radio frequency carriers are modulated to transmit audio-frequency signals to a radio receiver. These are also the applications that usually come to mind first when thinking about modulation. However, modulation is important in other ways.

A violinist can rapidly vary the point where pressure is being applied to the strings to produce a fluctuation in pitch called "vibrato." By varying the pressure on the bow, a fluctuation in volume can be produced called "tremolo." These, too, are examples of modulation. Electronic musicians employ low-frequency oscillators (LFOs) to produce fluctuating electric currents that modulate the acoustic frequency waves generated by an instrument and create the effect of acoustic sound. Most electronic keyboards have a "mod" or "modulation" wheel built in, which permits the keyboardist to vary the frequency of the LFOs during a performance. Other settings will determine whether it is pitch, volume, or both that are being varied and by how much.

Modulation techniques can be used to synthesize entirely new voices. When a signal modulates the amplitude of a carrier, additional waves are generated that are called "sidebands." These occur at frequencies that are the sum and difference of the carrier and signal frequencies. For example, if the signal is 10 hertz and the carrier is 100 hertz, the lower sideband will be at 90 hertz and the upper sideband will be at 110 hertz. If a signal consists of several frequencies, sidebands will be generated for each. The relative strengths of the carrier and the sidebands will vary depending on how much the carrier wave is modulated. The result is a new sound, which may be quite unlike the original signal or carrier.

Natural modulation also occurs. Records of some natural phenomena that recur frequently can reveal intriguing information when analyzed as signals that have been modulated at various frequencies. For example, researchers are looking for evidence of the eleven-year sunspot cycle in temperature, precipitation, and other climatological data. If they find it, the sunspot cycle will be modulating the annual cycles.

Another naturally occurring example of amplitude modulation comes from tidal data. Because the tide-producing forces are greatest when the Sun, Moon, and Earth are in alignment (during the new moon and full moon), tidal records show a strong amplitude modulation with a period of the synodic (lunar) month. Other forces produce weaker signals. For example, lunar tide-producing forces are greatest during the Moon's closest approach to Earth (perigee), which has a period called the sidereal month, and solar tide-producing forces are greatest when Earth is closest to the Sun (perihelion), which has an annual period. The effects of each of these forces and several others can be identified in tidal data because each has a characteristic frequency or period. The longest that can be easily seen is the 18.6-year period in which the lunar orbit precesses. To analyze such records, it must be determined what periods are present and how significant each period's contribution is. In the case of tidal data, this has been done and has resulted in an elegant theory of the tides.

Although AM and FM continue to be the most popular modulation techniques for general broadcasting, they can be inefficient in their use of the radio frequency spectrum. As mentioned, AM produces two sidebands somewhat separated from the carrier frequency. Each of these and the modulated carrier contain all the information originally in the signal, so it can be useful to simply transmit one sideband. This is done by filtering out the carrier and unwanted sideband after modulation has occurred. The result is called single sideband (SSB) modulation. In crowded parts of the spectrum such as the amateur radio bands, SSB is popular because its narrow bandwidth permits more users within the same frequency range.

Many signals can be reasonably reconstructed without being sent in their entirety. Just as a child's dot-to-dot puzzle represents an entire image through a collection of dots, a waveform, even a quite complicated one, can be reconstructed by connecting a number of dots lifted from it. By selecting dots along the wave with a constant interval of time between them, called the "sampling rate," the wave can be represented with a series of numbers giving the amplitude at each interval. Modifying a carrier wave to send this series of numbers instead of the actual waveform is called pulse code modulation (PCM). Frequency content determines the sampling rate. For intelligible speech, a frequency range of 4,000 hertz is sufficient, and this can be accurately sampled at a rate of 8,000 samples per second. To convey all of the information in high-fidelity sound, with a frequency range of about 22,050 hertz, a sampling rate of 44,100 samples per second is required. The precision of these numbers controls how perfectly the original waveform can be reproduced. This precision is usually referred to in terms of the number of binary bits used to record it. Therefore, an eight-bit sound has its waveform recorded with a precision of about 1 part in 256, whereas a 16-bit sound (the standard for music CDs) has its waveform recorded with a precision of about 1 part in 65,536. Pulse code modulation is the process by which an analog signal is converted into a digital one.

Modulation puts information into a carrier. A variety of factors can add noise to the modulated carrier. By adding additional information to the signal, the information can be characterized in ways that will help separate the noise from the signal when it is demodulated or at least reveal if the signal has been received without error.

Applications

Modulation is such a useful process that countless applications exist. To provide some indication of what modulation can accomplish, consider these two situations in which the carrier is in the audible range: the artificial production of a bell-like sound and the transmission of computer-generated data over telephone lines.

The sound of a bell playing a tone at 440 hertz (the A above middle C) is distinctly different from the sound of an electronic oscillator playing the same note. Much of the difference can be attributed to partials (sometimes called "overtones") generated at frequencies above 440 hertz. Some of these partials will be at multiples of small whole-number fractions of 440 (such as 660, 880, and 1320 hertz), but others will be "inharmonic partials," not simple ratios to the frequency of the note being played. Most of these partials do not persist for very long. When the bell is first struck, all sorts of frequencies are present, but as the vibrations go around and around the bell, many will cancel each other out. Only those that travel an integral number of times around the bell will reinforce each other. Therefore, the sound of a bell starts with a very rich spectrum but evolves into a very sparse one, often with only the fundamental sound persisting. This effect is re-created by the word "ding," which emulates the sound of a bell.

To create a similar sound electronically, a variation of amplitude modulation called "ring modulation" is used. In normal amplitude modulation, in the absence of modulation, the carrier is transmitted at its normal amplitude. As modulation occurs, this amplitude may increase or decrease and reaches zero only when the amplitude of the signal is the same magnitude as the amplitude of the carrier and of opposite sign. In ring modulation, the amplitude of the carrier is directly proportional to the amplitude of the signal. If there is no signal, there is no carrier. In this case, all the power is put in the sidebands and none in the carrier. If the carrier were a sine wave with frequency m and the signal a sine wave with frequency n, then after ring modulation, there would be two sine waves with frequencies m+n and m-n. Modulating amplitude causes a shift in frequencies. If the signal also had a partial at frequency 2n and the carrier had a partial at frequency 2n and the carrier had a partial at frequency 2m, ring modulation would result in eight sine waves with frequencies of m+n, m+2n, m-n, m-2n, 2m+n, 2m+2n, 2m-n, and 2m-2n. Although a few of these sine waves might be related harmonically, most would not. This is an efficient means of generating a rich spectrum electronically. Controlling the intensity of the modulation with a time-varying envelope allows the production of a rich spectrum of sound that--just like a real bell--has many initial inharmonic partials that taper off.

Although modulation is a powerful way of producing new, pleasant, sounds, it can also modify sounds in ways that only an electronic device can understand. The word "modem" is short for modulator, demodulator. A modem's function is to take the digital data from one computer and use it to modulate an audio signal that can be transmitted over ordinary telephone lines to another modem, which will demodulate the signal and send an exact copy of the original digital data to a second computer. As long as the modems at both ends of the telephone line use the same technique to modulate and demodulate the signal, information will be transferred successfully.

A telephone line can transmit frequencies from about 200 hertz to 3,600 hertz. Modems modulate a tone at a frequency near the center of this, often at 1,800 hertz. Each second is divided into a series of pulses. In early modems, during each pulse the carrier could be either on or off. This is similar to sending Morse code and, in fact, is called "on/off keying." Binary data was thus transmitted with one bit per pulse, and early modems raced along at 300 bits per second. As technology improved, the length of a pulse was shortened, permitting more pulses per second, but eventually a limit was reached. This limit is imposed by the physical characteristics of the telephone lines already installed throughout the world. To achieve higher bit rates, improvements in modulation techniques would be required.

Those pulses can be used to transmit more information. A simple on/off keying says a carrier is either present or absent for each pulse. If pulses are permitted to have other attributes besides existence or nonexistence, additional information can be conveyed. Any attributes can serve this purpose as long as modems on both ends of the telephone line use the same ones and interpret them similarly. Amplitudes, frequencies, and phase angles have been the most popular. To maintain the advantages of digital data transmission, only discrete steps in any parameter should be used. Modulation occurs and information is conveyed by shifts between these steps. Therefore, for example, in amplitude-shift keying (ASK), two, four, or eight levels of the carrier amplitude may be used. (On/off keying is just ASK with only two amplitudes.) In frequency-shift keying (FSK), discrete offsets are used in the carrier frequency. Phase can also be modulated, but errors are reduced if the difference in phase angle between one pulse and the next carries the information rather than the absolute phase angle. Differential phase-shift keying (DPSK) is the modulation technique that does this.

By selecting among four phase angles, modems became able to transmit 2,400 bits per second. With eight phase angles, they reached 4,800 bits per second. Phase and amplitude can be varied independently, so both parameters can be modulated. With four choices of phase angle and four amplitude levels, for a total of sixteen possible states, modems reached 9,600 bits per second. Pulse amplitude modulation evolved into quadrature amplitude modulation. All of these were replaced by trellis code modulation (TCM). Speeds went to 14,400, then 28,800, and then 33,600 bits per second.

Modern modems are a marvel of technology, employing almost unimaginably complex modulation systems to ensure that each pulse of sound traveling down telephone lines carries the most information possible. As each new modulation method was developed, modem manufacturers came to an agreement on just how it was to work, and a new standard was published. Manufacturers could then design equipment to meet the specifications of that standard and know that their modems would be able to communicate with all other modems employing that standard. All the squeaking, honking, hissing, and beeping that is heard as a user logs on using a modem is the conversation between the user's modem and the one to which the user is connecting regarding the modulation standard they will use to send their data back and forth.

Context

A signal modifies a carrier wave by modulating it, and this modulated wave can be modified further. Modulation produces sidebands at different frequencies from the original so that the frequency of the modulated carrier can be shifted. If different voice signals are shifted by varying amounts, they can be moved to much higher frequencies where they can occupy tiny portions of the spectrum. In this way, a number of conversations can be multiplexed into one signal. In fact, 13,200 voice channels can be sent as one signal with a bandwidth of 62 million hertz. This signal cannot be sent out over ordinary telephone lines, of course, as each line has a bandwidth of only about 4,000 hertz. However, if coaxial cable or fiber-optic cable is used, these densities are practical.

The history of the telephone industry has been a history of increasingly complex modulation schemes. This history is being repeated in the world of digital data. As the Internet, a system of interconnected computers around the world, has become popular, its use has grown exponentially. Improvement in modulation techniques has permitted the information superhighway to carry all the additional traffic.

Principal terms

AMPLITUDE: The maximum displacement of a wave from its point of equilibrium

AMPLITUDE MODULATION (AM): Adjusting the amplitude of a carrier wave so that excursions above and below its nominal value are in proportion to the amplitude of the modulating signal

CARRIER: The wave that is modulated by the signal

DEMODULATION: The process of recovering a signal from a modulated carrier

FREQUENCY: The number of oscillations of a wave occurring during a unit of time; the usual unit of frequency is the hertz (Hz), defined as 1 oscillation per second

FREQUENCY MODULATION (FM): Adjusting the frequency of a carrier wave so that excursions above and below its average value are in proportion to the amplitude of the modulating signal

SIGNAL: The wave containing the information that will be used to modulate the carrier

Bibliography

Dodge, Charles, and Thomas A. Jerse. Computer Music: Synthesis, Composition, and Performance. New York: Macmillan, 1985. A standard text on computer music; the treatment of frequency modulation synthesis presented is exceptional. Although littered with occasional mathematical contrivances with which the average reader will not be familiar, the development and the potential power of this method of musical synthesis still comes through clearly. Suitable for college-level readers.

Pierce, John R., and Michael A. Noll. Signals: The Science of Telecommunications. New York: Scientific American Library, 1990. An excellent treatment of all aspects of telecommunications technology, written in an engaging, easy-to-read, concise manner. Explains what modulation is, why it is done, how it is done in many different applications, and how it is likely to improve in the future. Equations are carefully avoided, mathematical concepts are fully explained, and many graphs and figures are included to illustrate the subject matter. Suitable for high-school readers.

Pressing, Jeff. Synthesizer Performance and Real-Time Techniques. Madison, Wis.: A-R Editions, 1992. Focusing on how to perform interesting music with electronic devices, this book gives instructions on how to use low-frequency oscillators and modulation wheels common on modern electronic instruments. Shows how modulation can be used to produce interesting musical effects. Also includes some discussion of modulation synthesis techniques. Suitable for high-school readers.

Strange, Allen. Electronic Music: Systems, Techniques, and Controls. Dubuque, Iowa: Wm. C. Brown, 1972. Chapters on amplitude modulation and frequency modulation present an excellent overview on some of the ways in which modulation is used by electronic musicians. Not very technical, but sufficiently quantitative to be useful, these discussions frequently refer to recorded works that illustrate the techniques involved. Clearly written and illustrated with plenty of block drawings, this book is suitable for high-school readers.