Amplitude

This article is about amplitude in classical physics. For other uses, seeAmplitude (disambiguation).

Theamplitudeof aperiodicvariableis a measure of its change in a singleperiod(such astimeorspatial period). The amplitude of a non-periodic signal is itsmagnitudecompared with a reference value. There are various definitions of amplitude (see below), which are allfunctionsof the magnitude of the differences between the variable'sextreme values.In older texts, thephaseof a periodic function is sometimes called the amplitude.

Definitions

Asinusoidalcurve

1. Peak amplitude ($\scriptstyle {\hat {u}}$),
2. Peak-to-peak amplitude ($\scriptstyle 2{\hat {u}}$),
3. Root mean square amplitude ($\scriptstyle {\hat {u}}/{\sqrt {2}}$),
4. Wave period(not an amplitude)

Peak amplitude and semi-amplitude

For symmetric periodic waves, likesine wavesortriangle waves,peak amplitudeandsemi amplitudeare the same.

Peak amplitude

Inaudio system measurements,telecommunicationsand others where themeasurandis a signal that swings above and below a reference value but is notsinusoidal,peak amplitude is often used. If the reference is zero, this is the maximumabsolute valueof 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. The majority of scientific literatureemploys the termamplitudeorpeak amplitudeto mean semi-amplitude.

It is the most widely used measure of orbital wobble inastronomyand the measurement of smallradial velocitysemi-amplitudes of nearby stars is important in the search forexoplanets(seeDoppler spectroscopy).

Ambiguity

In general, the use ofpeak amplitudeis 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 (thepeak-to-peak amplitude) and then divided by two (thesemi-amplitude). In electrical engineering, the usual solution to this ambiguity is to measure the amplitude from a defined reference potential (such asgroundor 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(abbreviatedp–porPtPorPtoP) is the change between peak (highest amplitude value) andtrough(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 anoscilloscope.Peak-to-peak is a straightforward measurement on an oscilloscope, the peaks of the waveform being easily identified and measured against thegraticule.This remains a common way of specifying amplitude, but sometimes other measures of amplitude are more appropriate.

Root mean square amplitude

Further information:RMS of common waveforms

Root mean square(RMS) amplitude is used especially inelectrical engineering:the RMS is defined as thesquare rootof themeanover time of the square of the vertical distance of the graph from the rest state; i.e. the RMS of the AC waveform (with noDC 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, theaveragepowertransmitted by an acoustic orelectromagnetic waveor by an electrical signal is proportional to the square of the RMS amplitude (and not, in general, to the square of the peak amplitude).

Foralternating currentelectric power,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 adirect currentin 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 commonvoltmetersare 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 onwaveform.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 inradio frequencymeasurements, where instruments measured the heating effect in a resistor to measure a current. The advent ofmicroprocessor-controlled meters capable of calculating RMS bysamplingthe waveform has made true RMS measurement commonplace.

Pulse amplitude

In telecommunications,pulse amplitudeis themagnitudeof apulseparameter, such as thevoltagelevel,currentlevel,field intensity,orpowerlevel.

Pulse amplitude is measured with respect to a specified reference and therefore should be modified by qualifiers, such asaverage,instantaneous,peak,orroot-mean-square.

Pulse amplitude also applies to the amplitude offrequency- andphase-modulatedwaveform envelopes.

Formal representation

In this simplewave equation

$x=A\sin(\ Omega [t-K])+b\,$

• $A$is the amplitude (orpeak amplitude),
• $x$is the oscillating variable,
• $\ Omega$isangular 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 astring,or in a medium such aswater,the amplitude is adisplacement.

The amplitude of sound waves and audio signals (which relates to the volume) conventionally refers to the amplitude of theair pressurein the wave, but sometimes the amplitude of thedisplacement(movements of the air or the diaphragm of aspeaker) is described.Thelogarithmof the amplitude squared is usually quoted indB,so a null amplitude corresponds to −∞dB.Loudnessis related to amplitude andintensityand is one of the most salient qualities of a sound, although in general sounds it can be recognizedindependently of amplitude.The square of the amplitude is proportional to the intensity of the wave.

Forelectromagnetic radiation,the amplitude of aphotoncorresponds to the changes in theelectric fieldof the wave. However, radio signals may be carried by electromagnetic radiation; the intensity of the radiation (amplitude modulation) or the frequency of the radiation (frequency modulation) is oscillated and then the individual oscillations are varied (modulated) to produce the signal.

Amplitude envelopes

Amplitudeenveloperefers 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 amplitudeproportionenvelopes, 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

• Atmospheric temperature § Temperature range
• Bodythermal amplitude
• Complex amplitude
• Pitch (music)
• Wave height
• Wavesand their properties:
  • Crest factor
  • Envelope
  • Frequency
  • Wavelength