Crest factor is a parameter of awaveform, such asalternating current or sound, showing the ratio of peak values to the effective value. In other words, crest factor indicates how extreme the peaks are in a waveform. Crest factor 1 indicates no peaks, such asdirect current or asquare wave. Higher crest factors indicate peaks, for example sound waves tend to have high crest factors.

Crest factor is thepeak amplitude of the waveform divided by theRMS value of the waveform.

Thepeak-to-average power ratio (PAPR) is the peak amplitude squared (giving the peakpower) divided by theRMS value squared (giving the averagepower).^[1] It is the square of the crest factor.

When expressed indecibels, crest factor and PAPR are equivalent, due to the way decibels arecalculated for power ratios vs amplitude ratios.

Crest factor and PAPR are thereforedimensionless quantities. While the crest factor is defined as a positivereal number, in commercial products it is also commonly stated as the ratio of two whole numbers, e.g., 2:1. The PAPR is most used in signal processing applications. As it is a power ratio, it is normally expressed indecibels (dB). The crest factor of the test signal is a fairly important issue inloudspeaker testing standards; in this context it is usually expressed in dB.^[2][3][4]

The minimum possible crest factor is 1, 1:1 or 0 dB.

This table provides values for somenormalizedwaveforms. All peak magnitudes have been normalized to 1.

Wave type	Waveform	RMS value	Crest factor	PAPR (dB)
DC		1	1	0.0 dB
Sine wave		${\displaystyle \frac{1}{\sqrt{2}}\approx 0.707}$[5]	${\displaystyle \sqrt{2}\approx 1.414}$	3.01 dB
Full-wave rectified sine		${\displaystyle \frac{1}{\sqrt{2}}\approx 0.707}$[5]	${\displaystyle \sqrt{2}\approx 1.414}$	3.01 dB
Half-wave rectified sine		${\displaystyle \frac{1}{2}=0.5}$[5]	${\displaystyle 2}$	6.02 dB
Triangle wave		${\displaystyle \frac{1}{\sqrt{3}}\approx 0.577}$	${\displaystyle \sqrt{3}\approx 1.732}$	4.77 dB
Square wave		1	1	0 dB
PWM signal V(t) ≥ 0.0 V		${\displaystyle \sqrt{\frac{t_1}{T}}}$[5]	${\displaystyle \sqrt{\frac{T}{t_1}}}$	${\displaystyle 20\log \left(\frac{T}{t_1}\right)}$ dB
QPSK		1	1	1.761 dB[6]
8PSK				3.3 dB[7]
π⁄4-DQPSK				3.0 dB[7]
OQPSK				3.3 dB[7]
8VSB				6.5–8.1 dB[8]
64QAM		${\displaystyle \sqrt{\frac{3}{7}}}$	${\displaystyle \sqrt{\frac{7}{3}}\approx 1.528}$	3.7 dB[9]
${\displaystyle \mathrm{\infty }}$-QAM		${\displaystyle \frac{1}{\sqrt{3}}\approx 0.577}$	${\displaystyle \sqrt{3}\approx 1.732}$	4.8 dB[9]
WCDMA downlink carrier				10.6 dB
OFDM			4	~12 dB
GMSK		1	1	0 dB
Gaussian noise		${\displaystyle \sigma }$[10][11]	${\displaystyle \mathrm{\infty }}$[12][13]	${\displaystyle \mathrm{\infty }}$ dB
Periodic chirp		${\displaystyle \frac{1}{\sqrt{2}}\approx 0.707}$	${\displaystyle \sqrt{2}\approx 1.414}$	3.01 dB

Notes:

1. Crest factors specified for QPSK, QAM, WCDMA are typical factors needed for reliable communication, not the theoretical crest factors which can be larger.

Many modulation techniques have been specifically designed to haveconstant envelope modulation, i.e., the minimum possible crest factor of 1:1.

In general, modulation techniques that have smaller crest factors usually transmit more bits per second than modulation techniques that have higher crest factors. This is because:

1. any givenlinear amplifier has some "peak output power"—some maximum possible instantaneous peak amplitude it can support and still stay in the linear range;
2. the average power of the signal is the peak output power divided by the crest factor;
3. the number of bits per second transmitted (on average) is proportional to the average power transmitted (Shannon–Hartley theorem).

Orthogonal frequency-division multiplexing (OFDM) is a very promising modulation technique; perhaps its biggest problem is its high crest factor.^[14][15] Many crest factor reduction techniques (CFR) have been proposed for OFDM.^[16][17][18] The reduction in crest factor results in a system that can either transmit more bits per second with the same hardware, or transmit the same bits per second withlower-power hardware (and therefore lower electricity costs^[19] and less expensive hardware), or both. Over the years, numerous model-driven approaches have been proposed to reduce the PAPR in communication systems. In recent years, there has been a growing interest in exploring data-driven models for PAPR reduction as part of ongoing research in end-to-end communication networks. These data-driven models offer innovative solutions and new avenues of exploration to address the challenges posed by high PAPR effectively. By leveraging data-driven techniques, researchers aim to enhance the performance and efficiency of communication networks by optimizing power utilization.^[20][21]

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Various methods for crest factor reduction exist, such as peak windowing,noise shaping, pulse injection and peak cancellation.

• Electrical engineering — for describing the quality of an AC power waveform
• Vibration analysis — for estimating the amount of impactwear in abearing^[22]
• Radio andaudio electronics — for estimating theheadroom required in a signal chain^[23][24]
  • Music has a widely varying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to12–18 dB of headroom, usually involvingaudio level compression), and 8–10 for an unprocessed recording(18–20 dB).^{[25][26][27][28]}
• Physiology — for analysing the sound ofsnoring^[29]

• Clipping (signal processing)
• Form factor (electronics)

 This article incorporatespublic domain material fromFederal Standard 1037C.General Services Administration. Archived fromthe original on 2022-01-22. (in support ofMIL-STD-188).

• Definition ofpeak-to-average ratio – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
• Definition ofcrest factor – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
• Peak-to-average power ratio (PAPR) of OFDM systems - tutorial

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