Amplitude
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The amplitude of a periodic variable is a measure of its change in a single period (such as
time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...
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 and semi-amplitude

For symmetric periodic waves, like sine waves or triangle waves, ''peak amplitude'' and ''semi amplitude'' are the same.


Peak amplitude

In
audio system measurements Audio system measurements are used to quantify audio system performance. These measurements are made for several purposes. Designers take measurements to specify the performance of a piece of equipment. Maintenance engineers make them to ensur ...
,
telecommunications Telecommunication, often used in its plural form or abbreviated as telecom, is the transmission of information over a distance using electronic means, typically through cables, radio waves, or other communication technologies. These means of ...
and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, 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 x 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), 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 the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...
and the measurement of small radial velocity 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 confirmed detection of an exoplanet was in 1992 around a pulsar, and the first detection around a main-sequence star was in 1995. A different planet, first det ...
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 or 0 V). Strictly speaking, this is no longer amplitude since there is the possibility that a constant ( DC component) is included in the measurement.


Peak-to-peak amplitude

Peak-to-peak amplitude (abbreviated p–p or PtP or PtoP) 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. Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against the graticule. 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, the root mean square (abbrev. RMS, or rms) of a set of values is the square root of the set's mean square. Given a set x_i, its RMS is denoted as either x_\mathrm or \mathrm_x. The RMS is also known as the quadratic mean (denote ...
(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 that use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
: the RMS is defined as the square root of the mean 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). 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 transmitted by an acoustic or electromagnetic wave 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 that 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 w ...
electric power Electric power is the rate of transfer of electrical energy within a electric circuit, circuit. Its SI unit is the watt, the general unit of power (physics), power, defined as one joule per second. Standard prefixes apply to watts as with oth ...
, 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 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. A ...
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. 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 measurements, where instruments measured the heating effect in a resistor to measure a current. The advent of
microprocessor A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, a ...
-controlled meters capable of calculating RMS by sampling the waveform has made true RMS measurement commonplace.


Pulse amplitude

In telecommunications, ''pulse amplitude'' is the magnitude of a pulse parameter, such as the
voltage Voltage, also known as (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
level, current level, field intensity, or power 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- and phase-modulated waveform envelopes.


Formal representation

In this simple wave equation :x = A \sin(\omega - K + b \ , *, A, is the amplitude (or peak amplitude), *x is the oscillating variable, *\omega is angular frequency, *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 is an inorganic compound with the chemical formula . It is a transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance. It is the main constituent of Earth's hydrosphere and the fluids of all known liv ...
, 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 air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The Standard atmosphere (unit), standard atmosphere (symbol: atm) is a unit of pressure defined as , whi ...
in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a speaker) is described. The
logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
of the amplitude squared is usually quoted in dB, so a null amplitude corresponds to −  dB. Loudness 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) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...
, 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 particles that can ...
corresponds to the changes in the
electric field An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...
of the wave. However, radio signals may be carried by electromagnetic radiation; the intensity of the radiation (
amplitude modulation Amplitude modulation (AM) is a signal modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the instantaneous amplitude of the wave is varied in proportion t ...
) or the frequency of the radiation ( frequency modulation) is oscillated and then the individual oscillations are varied (modulated) to produce the signal.


Amplitude envelopes

Amplitude envelope refers to the changes in the amplitude of a sound over time, and is an influential property as it affects perception of timbre. A flat tone has a steady state amplitude that remains constant during time, which is represented by a scalar. Other sounds can have percussive amplitude envelopes featuring an abrupt onset followed by an immediate exponential decay. Percussive amplitude envelopes are characteristic of various impact sounds: two wine glasses clinking together, hitting a drum, slamming a door, etc. where the amplitude is transient and must be represented as either a continuous function or a discrete vector. Percussive amplitude envelopes model many common sounds that have a transient loudness attack, decay, sustain, and release.


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

* *Body thermal amplitude * Complex amplitude * Pitch (music) * Wave height * Waves and their properties: ** Crest factor ** Envelope ** Frequency ** Wavelength


References

{{Authority control Physical quantities Sound Wave mechanics