HOME

TheInfoList



OR:

The amplitude of a periodic variable is a measure of its change in a single period (such as
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude.


Definitions


Peak amplitude & semi-amplitude

For symmetric periodic waves, like
sine wave A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often in ...
s,
square wave A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square wave, the transitions b ...
s or
triangle wave A triangular wave or triangle wave is a non-sinusoidal waveform named for its triangular shape. It is a periodic, piecewise linear, continuous real function. Like a square wave, the triangle wave contains only odd harmonics. However, ...
s ''peak amplitude'' and ''semi amplitude'' are the same.


Peak amplitude

In audio system measurements,
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
s and others where the
measurand Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...
is a signal that swings above and below a reference value but is not
sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...
, peak amplitude is often used. If the reference is zero, this is the maximum
absolute value In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...
of the signal; if the reference is a mean value (
DC component DC, D.C., D/C, Dc, or dc may refer to: Places * Washington, D.C. (District of Columbia), the capital and the federal territory of the United States * Bogotá, Distrito Capital, the capital city of Colombia * Dubai City, as distinct from t ...
), the peak amplitude is the maximum absolute value of the difference from that reference.


Semi-amplitude

Semi-amplitude means half of the peak-to-peak amplitude.Tatum, J. B.
Physics  – Celestial Mechanics
'' Paragraph 18.2.12. 2007. Retrieved 2008-08-22.
The majority of scientific literature employs the term ''amplitude'' or ''peak amplitude'' to mean semi-amplitude. It is the most widely used measure of orbital wobble in
astronomy Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
and the measurement of small
radial velocity The radial velocity or line-of-sight velocity, also known as radial speed or range rate, of a target with respect to an observer is the rate of change of the distance or range between the two points. It is equivalent to the vector projection ...
semi-amplitudes of nearby stars is important in the search for
exoplanet An exoplanet or extrasolar planet is a planet outside the Solar System. The first possible evidence of an exoplanet was noted in 1917 but was not recognized as such. The first confirmation of detection occurred in 1992. A different planet, init ...
s (see Doppler spectroscopy).


Ambiguity

In general, the use of ''peak amplitude'' is simple and unambiguous only for symmetric periodic waves, like a sine wave, a square wave, or a triangle wave. For an asymmetric wave (periodic pulses in one direction, for example), the peak amplitude becomes ambiguous. This is because the value is different depending on whether the maximum positive signal is measured relative to the mean, the maximum negative signal is measured relative to the mean, or the maximum positive signal is measured relative to the maximum negative signal (the ''peak-to-peak amplitude'') and then divided by two (the ''semi-amplitude''). In electrical engineering, the usual solution to this ambiguity is to measure the amplitude from a defined reference potential (such as
ground Ground may refer to: Geology * Land, the surface of the Earth not covered by water * Soil, a mixture of clay, sand and organic matter present on the surface of the Earth Electricity * Ground (electricity), the reference point in an electrical c ...
or 0 V). Strictly speaking, this is no longer amplitude since there is the possibility that a constant (
DC component DC, D.C., D/C, Dc, or dc may refer to: Places * Washington, D.C. (District of Columbia), the capital and the federal territory of the United States * Bogotá, Distrito Capital, the capital city of Colombia * Dubai City, as distinct from t ...
) is included in the measurement.


Peak-to-peak amplitude

Peak-to-peak amplitude (abbreviated p–p) is the change between peak (highest amplitude value) and trough (lowest amplitude value, which can be negative). With appropriate circuitry, peak-to-peak amplitudes of electric oscillations can be measured by meters or by viewing the waveform on an
oscilloscope An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetiti ...
. Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the
graticule Graticule may refer to: * An oscilloscope graticule scale * The reticle pattern in an optical instrument * Graticule (cartography), a grid of lines on a map See also * Grid (disambiguation) Grid, The Grid, or GRID may refer to: Common us ...
. This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate.


Root mean square amplitude

Root mean square In mathematics and its applications, the root mean square of a set of numbers x_i (abbreviated as RMS, or rms and denoted in formulas as either x_\mathrm or \mathrm_x) is defined as the square root of the mean square (the arithmetic mean of the ...
(RMS) amplitude is used especially in
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
: the RMS is defined as the
square root In mathematics, a square root of a number is a number such that ; in other words, a number whose '' square'' (the result of multiplying the number by itself, or  ⋅ ) is . For example, 4 and −4 are square roots of 16, because . ...
of the
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ar ...
over time of the square of the vertical distance of the graph from the rest state; i.e. the RMS of the AC waveform (with no
DC component DC, D.C., D/C, Dc, or dc may refer to: Places * Washington, D.C. (District of Columbia), the capital and the federal territory of the United States * Bogotá, Distrito Capital, the capital city of Colombia * Dubai City, as distinct from t ...
). For complicated waveforms, especially non-repeating signals like noise, the RMS amplitude is usually used because it is both unambiguous and has physical significance. For example, the ''average''
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
transmitted by an acoustic or
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
or by an electrical signal is proportional to the square of the RMS amplitude (and not, in general, to the square of the peak amplitude). For
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
electric power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions ...
, the universal practice is to specify RMS values of a sinusoidal waveform. One property of root mean square voltages and currents is that they produce the same heating effect as a
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or ev ...
in a given resistance. The peak-to-peak value is used, for example, when choosing rectifiers for power supplies, or when estimating the maximum voltage that insulation must withstand. Some common
voltmeter A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit. ...
s are calibrated for RMS amplitude, but respond to the average value of a rectified waveform. Many digital voltmeters and all moving coil meters are in this category. The RMS calibration is only correct for a sine wave input since the ratio between peak, average and RMS values is dependent on
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
. If the wave shape being measured is greatly different from a sine wave, the relationship between RMS and average value changes. True RMS-responding meters were used in
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the up ...
measurements, where instruments measured the heating effect in a resistor to measure a current. The advent of
microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circ ...
controlled meters capable of calculating RMS by sampling the waveform has made true RMS measurement commonplace.


Pulse amplitude

In
telecommunication Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
, ''pulse amplitude'' is the magnitude of a
pulse In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the n ...
parameter, such as the
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
level,
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
level,
field intensity In physics, field strength means the ''magnitude'' of a vector-valued field (e.g., in volts per meter, V/m, for an electric field ''E''). For example, an electromagnetic field results in both electric field strength and magnetic field strength. As ...
, or
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
level. Pulse amplitude is measured with respect to a specified reference and therefore should be modified by qualifiers, such as ''average'', ''instantaneous'', ''peak'', or ''root-mean-square''. Pulse amplitude also applies to the amplitude of
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
- and phase-modulated
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
envelopes.


Formal representation

In this simple
wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields — as they occur in classical physics — such as mechanical waves (e.g. water waves, sound waves and ...
:x = A \sin(\omega - K + b \ , *A is the amplitude (or
peak amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of ampli ...
), *x is the oscillating variable, *\omega is
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit ti ...
, *t is time, *K and b are arbitrary constants representing time and displacement offsets respectively.


Units

The units of the amplitude depend on the type of wave, but are always in the same units as the oscillating variable. A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case. For waves on a string, or in a medium such as
water Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as ...
, the amplitude is a displacement. The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of the
air pressure Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars ...
in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a
speaker Speaker may refer to: Society and politics * Speaker (politics), the presiding officer in a legislative assembly * Public speaker, one who gives a speech or lecture * A person producing speech: the producer of a given utterance, especially: ** In ...
) is described. The
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 ...
of the amplitude squared is usually quoted in dB, so a null amplitude corresponds to −  dB.
Loudness In acoustics, loudness is the subjective perception of sound pressure. More formally, it is defined as, "That attribute of auditory sensation in terms of which sounds can be ordered on a scale extending from quiet to loud". The relation of ph ...
is related to amplitude and intensity and is one of the most salient qualities of a sound, although in general sounds it can be recognized independently of amplitude. The square of the amplitude is proportional to the intensity of the wave. For
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
, the amplitude of a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alwa ...
corresponds to the changes in the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field ...
of the wave. However, radio signals may be carried by electromagnetic radiation; the intensity of the radiation (
amplitude modulation Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to ...
) or the frequency of the radiation (
frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog ...
) is oscillated and then the individual oscillations are varied (modulated) to produce the signal.


Transient amplitude envelopes

A steady state amplitude remains constant during time, thus is represented by a scalar. Otherwise, the amplitude is transient and must be represented as either a continuous function or a discrete vector. For audio, transient amplitude envelopes model signals better because many common sounds have a transient loudness attack, decay, sustain, and release. Other parameters can be assigned steady state or transient amplitude envelopes: high/low frequency/amplitude modulation, Gaussian noise, overtones, etc.


Amplitude normalization

With waveforms containing many overtones, complex transient timbres can be achieved by assigning each overtone to its own distinct transient amplitude envelope. Unfortunately, this has the effect of modulating the loudness of the sound as well. It makes more sense to separate loudness and harmonic quality to be parameters controlled independently of each other. To do so, harmonic amplitude envelopes are frame-by-frame normalized to become amplitude ''proportion'' envelopes, where at each time frame all the harmonic amplitudes will add to 100% (or 1). This way, the main loudness-controlling envelope can be cleanly controlled. In Sound Recognition, max amplitude normalization can be used to help align the key harmonic features of 2 alike sounds, allowing similar timbres to be recognized independent of loudness.


See also

* Complex amplitude *
Wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...
s and their properties: **
Envelope An envelope is a common packaging item, usually made of thin, flat material. It is designed to contain a flat object, such as a letter or card. Traditional envelopes are made from sheets of paper cut to one of three shapes: a rhombus, a sh ...
**
Frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
**
Wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
**
Crest factor Crest or CREST may refer to: Buildings *The Crest (Huntington, New York), a historic house in Suffolk County, New York *"The Crest", an alternate name for 63 Wall Street, in Manhattan, New York * Crest Castle (Château Du Crest), Jussy, Switzer ...
* Amplitude modulation *Body thermal amplitude * Atmospheric thermal amplitude


Notes

{{Authority control Physical quantities Sound Wave mechanics