Frequency is the number of occurrences of a repeating event per unit of time. It is referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency; the period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example: if a newborn baby's heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals, radio waves, light. For cyclical processes, such as rotation, oscillations, or waves, frequency is defined as a number of cycles per unit time. In physics and engineering disciplines, such as optics and radio, frequency is denoted by a Latin letter f or by the Greek letter ν or ν; the relation between the frequency and the period T of a repeating event or oscillation is given by f = 1 T.
The SI derived unit of frequency is the hertz, named after the German physicist Heinrich Hertz. One hertz means. If a TV has a refresh rate of 1 hertz the TV's screen will change its picture once a second. A previous name for this unit was cycles per second; the SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. 60 rpm equals one hertz. As a matter of convenience and slower waves, such as ocean surface waves, tend to be described by wave period rather than frequency. Short and fast waves, like audio and radio, are described by their frequency instead of period; these used conversions are listed below: Angular frequency denoted by the Greek letter ω, is defined as the rate of change of angular displacement, θ, or the rate of change of the phase of a sinusoidal waveform, or as the rate of change of the argument to the sine function: y = sin = sin = sin d θ d t = ω = 2 π f Angular frequency is measured in radians per second but, for discrete-time signals, can be expressed as radians per sampling interval, a dimensionless quantity.
Angular frequency is larger than regular frequency by a factor of 2π. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes. E.g.: y = sin = sin d θ d x = k Wavenumber, k, is the spatial frequency analogue of angular temporal frequency and is measured in radians per meter. In the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has an inverse relationship to the wavelength, λ. In dispersive media, the frequency f of a sinusoidal wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave: f = v λ. In the special case of electromagnetic waves moving through a vacuum v = c, where c is the speed of light in a vacuum, this expression becomes: f = c λ; when waves from a monochrome source travel from one medium to another, their frequency remains the same—only their wavelength and speed change. Measurement of frequency can done in the following ways, Calculating the frequency of a repeating event is accomplished by counting the number of times that event occurs within a specific time period dividing the count by the length of the time period.
For example, if 71 events occur within 15 seconds the frequency is: f = 71 15 s ≈ 4.73 Hz If the number of counts is not large, it is more accurate to measure the time interval for a predetermined number of occurrences, rather than the number of occurrences within a specified time. The latter method introduces a random error into the count of between zero and one count, so on average half a count; this is called gating error and causes an average error in the calculated frequency of Δ f = 1 2 T
A spark-gap transmitter is an obsolete type of radio transmitter which generates radio waves by means of an electric spark. Spark-gap transmitters were the first type of radio transmitter, were the main type used during the wireless telegraphy or "spark" era, the first three decades of radio, from 1887 to the end of World War 1. German physicist Heinrich Hertz built the first experimental spark-gap transmitters in 1887, with which he discovered radio waves and studied their properties. A fundamental limitation of spark-gap transmitters is that they generate a series of brief transient pulses of radio waves called damped waves. So spark-gap transmitters could not transmit audio, instead transmitted information by radiotelegraphy; the first practical spark gap transmitters and receivers for radiotelegraphy communication were developed by Guglielmo Marconi around 1896. One of the first uses for spark-gap transmitters was on ships, to communicate with shore and broadcast a distress call if the ship was sinking.
They played a crucial role in maritime rescues such as the 1912 RMS Titanic disaster. After World War 1, transmitters based on vacuum tubes were developed, which were cheaper and produced continuous waves which had a greater range, produced less interference, could carry audio, making spark transmitters obsolete by 1920; the radio signals produced by spark-gap transmitters are electrically "noisy". This type of radio emission has been prohibited by international law since 1934. Electromagnetic waves are radiated by electric charges. Radio waves, electromagnetic waves of radio frequency, can be generated by time-varying electric currents, consisting of electrons flowing through a conductor which change their velocity, thus accelerating. A capacitance discharged through an electric spark across a spark gap between two conductors was the first device known which could generate radio waves; the spark itself doesn't produce the radio waves, it serves to excite resonant radio frequency oscillating electric currents in the conductors of the attached circuit.
The conductors radiate the energy in this oscillating current as radio waves. Due to the inherent inductance of circuit conductors, the discharge of a capacitor through a low enough resistance is oscillatory. A practical spark gap transmitter consists of these parts: A high-voltage transformer, to transform the low-voltage electricity from the power source, a battery or electric outlet, to a high enough voltage to jump across the spark gap; the transformer charges the capacitor. In low-power transmitters powered by batteries this was an induction coil. One or more resonant circuits which create radio frequency electrical oscillations when excited by the spark. A resonant circuit consists of a capacitor which stores high-voltage electricity from the transformer, a coil of wire called an inductor or tuning coil, connected together; the values of the capacitance and inductance determine. The earliest spark-gap transmitters before 1897 did not have a resonant circuit. Most spark transmitters had two resonant circuits coupled together with an air core transformer called a resonant transformer or oscillation transformer.
This was called an inductively-coupled transmitter. The spark gap and capacitor connected to the primary winding of the transformer made one resonant circuit, which generated the oscillating current; the oscillating current in the primary winding created an oscillating magnetic field that induced current in the secondary winding. The antenna and ground were connected to the secondary winding; the capacitance of the antenna resonated with the secondary winding to make a second resonant circuit. The two resonant circuits were tuned to the same resonant frequency; the advantage of this circuit was that the oscillating current persisted in the antenna circuit after the spark stopped, creating long, ringing damped waves, in which the energy was concentrated in a narrower bandwidth, creating less interference to other transmitters. A spark gap which acts as a voltage-controlled switch in the resonant circuit, discharging the capacitor through the coil. An antenna, a metal conductor such as an elevated wire, that radiates the power in the oscillating electric currents from the resonant circuit into space as radio waves.
A telegraph key to switch the transmitter on and off to communicate messages by Morse code The transmitter works in a rapid repeating cycle in which the capacitor is charged to a high voltage by the transformer and discharged through the coil by a spark across the spark gap. The impulsive spark excites the resonant circuit to "ring" like a bell, producing a brief oscillating current, radiated as electromagnetic waves by the antenna; the transmitter repeats this cycle at a rapid rate, so the spark appeared continuous, the radio signal sounded like a whine or buzz in a radio receiver. The cycle begins when current from the transformer charges up the capacitor, storing electric charge on its plates. While
A spark gap consists of an arrangement of two conducting electrodes separated by a gap filled with a gas such as air, designed to allow an electric spark to pass between the conductors. When the potential difference between the conductors exceeds the breakdown voltage of the gas within the gap, a spark forms, ionizing the gas and drastically reducing its electrical resistance. An electric current flows until the path of ionized gas is broken or the current reduces below a minimum value called the "holding current"; this happens when the voltage drops, but in some cases occurs when the heated gas rises, stretching out and breaking the filament of ionized gas. The action of ionizing the gas is violent and disruptive leading to sound and heat. Spark gaps were used in early electrical equipment, such as spark gap radio transmitters, electrostatic machines, X-ray machines, their most widespread use today is in spark plugs to ignite the fuel in internal combustion engines, but they are used in lightning arresters and other devices to protect electrical equipment from high-voltage transients.
The light emitted by a spark does not come from the current of electrons itself, but from the material medium fluorescing in response to collisions from the electrons. When electrons collide with molecules of air in the gap, they excite their orbital electrons to higher energy levels; when these excited electrons fall back to their original energy levels, they emit energy as light. It is impossible for a visible spark to form in a vacuum. Without intervening matter capable of electromagnetic transitions, the spark will be invisible. Spark gaps are essential to the functioning of a number of electronic devices. A spark plug uses a spark gap to initiate combustion; the heat of the ionization trail, but more UV radiation and hot free electrons ignite a fuel-air mixture inside an internal combustion engine, or a burner in a furnace, oven, or stove. The more UV radiation is produced and spread into the combustion chamber, the further the combustion process proceeds. Spark gaps are used to prevent voltage surges from damaging equipment.
Spark gaps are used in high-voltage switches, large power transformers, in power plants and electrical substations. Such switches are constructed with a large, remote-operated switching blade with a hinge as one contact and two leaf springs holding the other end as second contact. If the blade is opened, a spark may keep the connection between spring conducting; the spark ionizes the air, which becomes conductive and allows an arc to form, which sustains ionization and hence conduction. A Jacob's ladder on top of the switch will cause the arc to rise and extinguish. One might find small Jacob's ladders mounted on top of ceramic insulators of high-voltage pylons; these are sometimes called horn gaps. If a spark should manage to jump over the insulator and give rise to an arc, it will be extinguished. Smaller spark gaps are used to protect sensitive electrical or electronic equipment from high-voltage surges. In sophisticated versions of these devices, a small spark gap breaks down during an abnormal voltage surge, safely shunting the surge to ground and thereby protecting the equipment.
These devices are used for telephone lines as they enter a building. Less sophisticated spark gaps are made using modified ceramic capacitors. A voltage surge causes a spark that jumps from lead wire to lead wire across the gap left by the sawing process; these low-cost devices are used to prevent damaging arcs between the elements of the electron gun within a cathode ray tube. Small spark gaps are common in telephone switchboards, as the long phone cables are susceptible to induced surges from lightning strikes. Larger spark gaps are used to protect power lines. Spark gaps are implemented on Printed Circuit Boards in mains power electronics products using two spaced exposed PCB traces; this is an zero cost method of adding crude overload protection to electronics products. Transils and trisils are the solid-state alternatives to spark gaps for lower-power applications. Neon bulbs are used for this purpose. A triggered spark gap in an air-gap flash is used to produce photographic light flashes in the sub-microsecond domain.
A spark radiates energy throughout the electromagnetic spectrum. Nowadays, this is regarded as illegal radio frequency interference and is suppressed, but in the early days of radio communications, this was the means by which radio signals were transmitted, in the unmodulated spark-gap transmitter. Many radio spark gaps include cooling devices, such as the rotary gap and heat sinks, since the spark gap becomes quite hot under continuous use at high power. A calibrated spherical spark gap will break down at a repeatable voltage, when corrected for air pressure and temperature. A gap between two spheres can provide a voltage measurement without any electronics or voltage dividers, to an accuracy of about 3%. A spark gap can be used to measure high voltage AC, DC, or pulses, but for short pulses, an ultraviolet light source or radioactive source may be put on one of the terminals to provide a source of electrons. Spark gaps may be used as electrical switches because they have two states with
Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, measure, infinite series, analytic functions. These theories are studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary techniques of analysis. Analysis may be distinguished from geometry. Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians. Early results in analysis were implicitly present in the early days of ancient Greek mathematics. For instance, an infinite geometric sum is implicit in Zeno's paradox of the dichotomy. Greek mathematicians such as Eudoxus and Archimedes made more explicit, but informal, use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids; the explicit use of infinitesimals appears in Archimedes' The Method of Mechanical Theorems, a work rediscovered in the 20th century.
In Asia, the Chinese mathematician Liu Hui used the method of exhaustion in the 3rd century AD to find the area of a circle. Zu Chongzhi established a method that would be called Cavalieri's principle to find the volume of a sphere in the 5th century; the Indian mathematician Bhāskara II gave examples of the derivative and used what is now known as Rolle's theorem in the 12th century. In the 14th century, Madhava of Sangamagrama developed infinite series expansions, like the power series and the Taylor series, of functions such as sine, cosine and arctangent. Alongside his development of the Taylor series of the trigonometric functions, he estimated the magnitude of the error terms created by truncating these series and gave a rational approximation of an infinite series, his followers at the Kerala School of Astronomy and Mathematics further expanded his works, up to the 16th century. The modern foundations of mathematical analysis were established in 17th century Europe. Descartes and Fermat independently developed analytic geometry, a few decades Newton and Leibniz independently developed infinitesimal calculus, which grew, with the stimulus of applied work that continued through the 18th century, into analysis topics such as the calculus of variations and partial differential equations, Fourier analysis, generating functions.
During this period, calculus techniques were applied to approximate discrete problems by continuous ones. In the 18th century, Euler introduced the notion of mathematical function. Real analysis began to emerge as an independent subject when Bernard Bolzano introduced the modern definition of continuity in 1816, but Bolzano's work did not become known until the 1870s. In 1821, Cauchy began to put calculus on a firm logical foundation by rejecting the principle of the generality of algebra used in earlier work by Euler. Instead, Cauchy formulated calculus in terms of geometric infinitesimals. Thus, his definition of continuity required an infinitesimal change in x to correspond to an infinitesimal change in y, he introduced the concept of the Cauchy sequence, started the formal theory of complex analysis. Poisson, Liouville and others studied partial differential equations and harmonic analysis; the contributions of these mathematicians and others, such as Weierstrass, developed the -definition of limit approach, thus founding the modern field of mathematical analysis.
In the middle of the 19th century Riemann introduced his theory of integration. The last third of the century saw the arithmetization of analysis by Weierstrass, who thought that geometric reasoning was inherently misleading, introduced the "epsilon-delta" definition of limit. Mathematicians started worrying that they were assuming the existence of a continuum of real numbers without proof. Dedekind constructed the real numbers by Dedekind cuts, in which irrational numbers are formally defined, which serve to fill the "gaps" between rational numbers, thereby creating a complete set: the continuum of real numbers, developed by Simon Stevin in terms of decimal expansions. Around that time, the attempts to refine the theorems of Riemann integration led to the study of the "size" of the set of discontinuities of real functions. "monsters" began to be investigated. In this context, Jordan developed his theory of measure, Cantor developed what is now called naive set theory, Baire proved the Baire category theorem.
In the early 20th century, calculus was formalized using an axiomatic set theory. Lebesgue solved the problem of measure, Hilbert introduced Hilbert spaces to solve integral equations; the idea of normed vector space was in the air, in the 1920s Banach created functional analysis. In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. Much of analysis happens in some metric space. Examples of analysis without a metric include functional analysis. Formally, a metric space is an ordered pair where M is a set
Morse code is a character encoding scheme used in telecommunication that encodes text characters as standardized sequences of two different signal durations called dots and dashes or dits and dahs. Morse code is named for Samuel F. B. Morse, an inventor of the telegraph; the International Morse Code encodes the 26 English letters A through Z, some non-English letters, the Arabic numerals and a small set of punctuation and procedural signals. There is no distinction between lower case letters; each Morse code symbol is formed by a sequence of dashes. The dot duration is the basic unit of time measurement in Morse code transmission; the duration of a dash is three times the duration of a dot. Each dot or dash within a character is followed by period of signal absence, called a space, equal to the dot duration; the letters of a word are separated by a space of duration equal to three dots, the words are separated by a space equal to seven dots. To increase the efficiency of encoding, Morse code was designed so that the length of each symbol is inverse to the frequency of occurrence in text of the English language character that it represents.
Thus the most common letter in English, the letter "E", has the shortest code: a single dot. Because the Morse code elements are specified by proportion rather than specific time durations, the code is transmitted at the highest rate that the receiver is capable of decoding; the Morse code transmission rate is specified in groups per minute referred to as words per minute. Morse code is transmitted by on-off keying of an information carrying medium such as electric current, radio waves, visible light or sound waves; the current or wave is present during time period of the dot or dash and absent during the time between dots and dashes. Morse code can be memorized, Morse code signalling in a form perceptible to the human senses, such as sound waves or visible light, can be directly interpreted by persons trained in the skill; because many non-English natural languages use other than the 26 Roman letters, Morse alphabets have been developed for those languages. In an emergency, Morse code can be generated by improvised methods such as turning a light on and off, tapping on an object or sounding a horn or whistle, making it one of the simplest and most versatile methods of telecommunication.
The most common distress signal is SOS – three dots, three dashes, three dots – internationally recognized by treaty. Early in the nineteenth century, European experimenters made progress with electrical signaling systems, using a variety of techniques including static electricity and electricity from Voltaic piles producing electrochemical and electromagnetic changes; these numerous ingenious experimental designs were precursors to practical telegraphic applications. Following the discovery of electromagnetism by Hans Christian Ørsted in 1820 and the invention of the electromagnet by William Sturgeon in 1824, there were developments in electromagnetic telegraphy in Europe and America. Pulses of electric current were sent along wires to control an electromagnet in the receiving instrument. Many of the earliest telegraph systems used a single-needle system which gave a simple and robust instrument. However, it was slow, as the receiving operator had to alternate between looking at the needle and writing down the message.
In Morse code, a deflection of the needle to the left corresponded to a dot and a deflection to the right to a dash. By making the two clicks sound different with one ivory and one metal stop, the single needle device became an audible instrument, which led in turn to the Double Plate Sounder System; the American artist Samuel F. B. Morse, the American physicist Joseph Henry, Alfred Vail developed an electrical telegraph system, it needed a method to transmit natural language using only electrical pulses and the silence between them. Around 1837, therefore, developed an early forerunner to the modern International Morse code. William Cooke and Charles Wheatstone in England developed an electrical telegraph that used electromagnets in its receivers, they obtained an English patent in June 1837 and demonstrated it on the London and Birmingham Railway, making it the first commercial telegraph. Carl Friedrich Gauss and Wilhelm Eduard Weber as well as Carl August von Steinheil used codes with varying word lengths for their telegraphs.
In 1841, Cooke and Wheatstone built a telegraph that printed the letters from a wheel of typefaces struck by a hammer. The Morse system for telegraphy, first used in about 1844, was designed to make indentations on a paper tape when electric currents were received. Morse's original telegraph receiver used a mechanical clockwork to move a paper tape; when an electrical current was received, an electromagnet engaged an armature that pushed a stylus onto the moving paper tape, making an indentation on the tape. When the current was interrupted, a spring retracted the stylus and that portion of the moving tape remained unmarked. Morse code was developed so that operators could translate the indentations marked on the paper tape into text messages. In his earliest code, Morse had planned to transmit only numerals and to use a codebook to look up each word according to the number, sent. However, the code was soon expanded by Alfred Vail in 1840 to include letters and special characters so it could be used more generally.
Vail estimated the frequency of use of letters in the English language by counting the movable type he found in the type-cases of a local newspaper in Morristown. The shorter marks were called "dots" and the longer ones "dashes", the letters most used were assigned the shorter sequences of dots and dashes; this code was used since 1844 and became known as Morse lan
In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space, carrying electromagnetic radiant energy. It includes radio waves, infrared, ultraviolet, X-rays, gamma rays. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light, which, in a vacuum, is denoted c. In homogeneous, isotropic media, the oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave; the wavefront of electromagnetic waves emitted from a point source is a sphere. The position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves of different frequency are called by different names since they have different sources and effects on matter. In order of increasing frequency and decreasing wavelength these are: radio waves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays.
Electromagnetic waves are emitted by electrically charged particles undergoing acceleration, these waves can subsequently interact with other charged particles, exerting force on them. EM waves carry energy and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them electromagnetic induction and electrostatic induction phenomena. In quantum mechanics, an alternate way of viewing EMR is that it consists of photons, uncharged elementary particles with zero rest mass which are the quanta of the electromagnetic force, responsible for all electromagnetic interactions.
Quantum electrodynamics is the theory of. Quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation; the energy of an individual photon is greater for photons of higher frequency. This relationship is given by Planck's equation E = hν, where E is the energy per photon, ν is the frequency of the photon, h is Planck's constant. A single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light; the effects of EMR upon chemical compounds and biological organisms depend both upon the radiation's power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize atoms or molecules or break chemical bonds; the effects of these radiations on chemical systems and living tissue are caused by heating effects from the combined energy transfer of many photons. In contrast, high frequency ultraviolet, X-rays and gamma rays are called ionizing radiation, since individual photons of such high frequency have enough energy to ionize molecules or break chemical bonds.
These radiations have the ability to cause chemical reactions and damage living cells beyond that resulting from simple heating, can be a health hazard. James Clerk Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry; because the speed of EM waves predicted by the wave equation coincided with the measured speed of light, Maxwell concluded that light itself is an EM wave. Maxwell's equations were confirmed by Heinrich Hertz through experiments with radio waves. According to Maxwell's equations, a spatially varying electric field is always associated with a magnetic field that changes over time. A spatially varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the electric field are always accompanied by a wave in the magnetic field in one direction, vice versa; this relationship between the two occurs without either type of field causing the other.
In fact, magnetic fields can be viewed as electric fields in another frame of reference, electric fields can be viewed as magnetic fields in another frame of reference, but they have equal significance as physics is the same in all frames of reference, so the close relationship between space and time changes here is more than an analogy. Together, these fields form a propagating electromagnetic wave, which moves out into space and need never again interact with the source; the distant EM field formed in this way by the acceleration of a charge carries energy with it that "radiates" away through space, hence the term. Maxwell's equations established that some charges and currents produce a local type of electromagnetic field near them that does not have the behaviour of EMR. Currents directly produce a magnetic field, but it is of a magnetic dipole type that dies out with distance from the current. In a similar manner, moving charges pushed apart in a conductor by a changing electrical potential produce an electric dipole type electric
Amplitude modulation is a modulation technique used in electronic communication, most for transmitting information via a radio carrier wave. In amplitude modulation, the amplitude of the carrier wave is varied in proportion to that of the message signal being transmitted; the message signal is, for example, a function of the sound to be reproduced by a loudspeaker, or the light intensity of pixels of a television screen. This technique contrasts with frequency modulation, in which the frequency of the carrier signal is varied, phase modulation, in which its phase is varied. AM was the earliest modulation method used to transmit voice by radio, it was developed during the first quarter of the 20th century beginning with Landell de Moura and Reginald Fessenden's radiotelephone experiments in 1900. It remains in use today in many forms of communication. AM is used to refer to mediumwave AM radio broadcasting. In electronics and telecommunications, modulation means varying some aspect of a continuous wave carrier signal with an information-bearing modulation waveform, such as an audio signal which represents sound, or a video signal which represents images.
In this sense, the carrier wave, which has a much higher frequency than the message signal, carries the information. At the receiving station, the message signal is extracted from the modulated carrier by demodulation. In amplitude modulation, the amplitude or strength of the carrier oscillations is varied. For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission; the audio waveform modifies the amplitude of the carrier wave and determines the envelope of the waveform. In the frequency domain, amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands; each sideband is equal in bandwidth to that of the modulating signal, is a mirror image of the other. Standard AM is thus sometimes called "double-sideband amplitude modulation" to distinguish it from more sophisticated modulation methods based on AM. One disadvantage of all amplitude modulation techniques is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal.
Increasing the received signal-to-noise ratio, say, by a factor of 10, thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation and digital radio where the effect of such noise following demodulation is reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts. Another disadvantage of AM is; the carrier signal contains none of the original information being transmitted. However its presence provides a simple means of demodulation using envelope detection, providing a frequency and phase reference to extract the modulation from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex and costly; the receiver may regenerate a copy of the carrier frequency from a reduced "pilot" carrier to use in the demodulation process.
With the carrier eliminated in double-sideband suppressed-carrier transmission, carrier regeneration is possible using a Costas phase-locked loop. This doesn't work however for single-sideband suppressed-carrier transmission, leading to the characteristic "Donald Duck" sound from such receivers when detuned. Single sideband is used in amateur radio and other voice communications both due to its power efficiency and bandwidth efficiency. On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers; the broadcaster absorbs the extra power cost to increase potential audience. An additional function provided by the carrier in standard AM, but, lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation.
On the other hand, with suppressed-carrier transmissions there is no transmitted power during pauses in the modulation, so the AGC must respond to peaks of the transmitted power during peaks in the modulation. This involves a so-called fast attack, slow decay circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program; this is acceptable for communications radios, where compression of the audio aids intelligibility. However it is undesired for music or normal broadcast programming, where a faithful reproduction of the original program, including its varying modulation levels, is expected. A trivial form of AM which can be used for transmitting binary data is on-off keying, the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence