Crest factor is a parameter of a waveform, such as alternating 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 as direct current or a square wave. Higher crest factors indicate peaks, for example sound waves tend to have high crest factors.
Crest factor is the peak amplitude of the waveform divided by the RMS value of the waveform.
The peaktoaverage power ratio (PAPR) is the peak amplitude squared (giving the peak power) divided by the RMS value squared (giving the average power).^{[1]} It is the square of the crest factor.
When expressed in decibels, crest factor and PAPR are equivalent, due to the way decibels are calculated for power ratios vs amplitude ratios.
Crest factor and PAPR are therefore dimensionless quantities. While the crest factor is defined as a positive real 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 in decibels (dB). The crest factor of the test signal is a fairly important issue in loudspeaker 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.
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Transcription
Examples
This table provides values for some normalized waveforms. 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  ^{[5]}  3.01 dB  
Fullwave rectified sine  ^{[5]}  3.01 dB  
Halfwave rectified sine  ^{[5]}  6.02 dB  
Triangle wave  4.77 dB  
Square wave  1  1  0 dB  
PWM signal V(t) ≥ 0.0 V 
^{[5]} 
dB  
QPSK  1  1  1.761 dB^{[6]}  
8PSK  3.3 dB^{[7]}  
π⁄4DQPSK  3.0 dB^{[7]}  
OQPSK  3.3 dB^{[7]}  
8VSB  6.5–8.1 dB^{[8]}  
64QAM  3.7 dB^{[9]}  
QAM  4.8 dB^{[9]}  
WCDMA downlink carrier  10.6 dB  
OFDM  4  ~12 dB  
GMSK  1  1  0 dB  
Gaussian noise  ^{[10]}^{[11]}  ^{[12]}^{[13]}  dB  
Periodic chirp  3.01 dB 
Notes:
 Crest factors specified for QPSK, QAM, WCDMA are typical factors needed for reliable communication, not the theoretical crest factors which can be larger.
Crest factor reduction
Many modulation techniques have been specifically designed to have constant 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:
 any given linear amplifier has some "peak output power"—some maximum possible instantaneous peak amplitude it can support and still stay in the linear range;
 the average power of the signal is the peak output power divided by the crest factor;
 the number of bits per second transmitted (on average) is proportional to the average power transmitted (Shannon–Hartley theorem).
Orthogonal frequencydivision 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 with lowerpower hardware (and therefore lower electricity costs^{[19]} and less expensive hardware), or both. Over the years, numerous modeldriven approaches have been proposed to reduce the PAPR in communication systems. In recent years, there has been a growing interest in exploring datadriven models for PAPR reduction as part of ongoing research in endtoend communication networks. These datadriven models offer innovative solutions and new avenues of exploration to address the challenges posed by high PAPR effectively. By leveraging datadriven techniques, researchers aim to enhance the performance and efficiency of communication networks by optimizing power utilization. ^{[20]}
Crest factor reduction methods
Various methods for crest factor reduction exist, such as peak windowing, noise shaping, pulse injection and peak cancellation.
Applications
 Electrical engineering — for describing the quality of an AC power waveform
 Vibration analysis — for estimating the amount of impact wear in a bearing^{[21]}
 Radio and audio electronics — for estimating the headroom required in a signal chain^{[22]}^{[23]}
 Music has a widely varying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to 12–18 dB of headroom, usually involving audio level compression), and 8–10 for an unprocessed recording (18–20 dB).^{[24]}^{[25]}^{[26]}^{[27]}
 Physiology — for analysing the sound of snoring^{[28]}
See also
References
 ^ "Wireless 101: Peak to average power ratio (PAPR)".
 ^ JBL Speaker Power Requirements, which is applying the IEC standard 2685, itself more recently renamed to 602685
 ^ AES22012 standard, Annex B (Informative) Crest Factor, pp. 1720 in the 20130211 printing
 ^ "Dr. ProAudio", Power handling, summarizes the various speaker standards
 ^ ^{a} ^{b} ^{c} ^{d} "RMS and Average Values for Typical Waveforms". Archived from the original on 20100123.
 ^ Palicot, Jacques; Louët, Yves. POWER RATIO DEFINITIONS AND ANALYSIS IN SINGLE CARRIER MODULATIONS (PDF). IETR/Supélec  Campus de Rennes. p. 2.
 ^ ^{a} ^{b} ^{c} "Read steer_rf_chapter1.pdf". Archived from the original on 20160322. Retrieved 20141211.
 ^ "Transitioning transmitters to COFDM". Archived from the original on 20090821. Retrieved 20090617.
 ^ ^{a} ^{b} R. Wolf; F. Ellinger; R.Eickhoff; Massimiliano Laddomada; Oliver Hoffmann (14 July 2011). Periklis Chatzimisios (ed.). Mobile Lightweight Wireless Systems: Second International ICST Conference, Mobilight 2010, May 1012, 2010, Barcelona, Spain, Revised Selected Papers. Springer. p. 164. ISBN 9783642166433. Retrieved 13 December 2012.
 ^ Op Amp Noise Theory and Applications Archived 20141130 at the Wayback Machine  10.2.1 rms versus PP Noise
 ^ Chapter 1 FirstOrder LowPass Filtered Noise  "The standard deviation of a Gaussian noise voltage is the rootmeansquare or rms value of the voltage."
 ^ Noise: Frequently Asked Questions  "Noise theoretically has an unbounded distribution so that it should have an infinite crest factor"
 ^ Telecommunications Measurements, Analysis, and Instrumentation, Kamilo Feher, section 7.2.3 Finite Crest Factor Noise
 ^ "Crest Factor Reduction of an OFDM/WiMAX Network".
 ^ "Low Crest Factor Modulation Techniques for Orthogonal Frequency Division Multiplexing (OFDM)" Archived 20170829 at the Wayback Machine.
 ^ R. Neil Braithwaite. "Crest Factor Reduction for OFDM Using Selective Subcarrier Degradation" Archived 20180806 at the Wayback Machine.
 ^ K. T. Wong, B. Wang & J.C. Chen, "OFDM PAPR Reduction by Switching Null Subcarriers & DataSubcarriers," Electronics Letters, vol. 47, no. 1, pp. 6263 January, 2011 Archived 20150923 at the Wayback Machine.
 ^ S.C. Thompson, "Constant Envelope OFDM Phase Modulation," PhD Dissertation, UC San Diego, 2005.
 ^ Nick Wells. "DVBT2 in relation to the DVBx2 Family of Standards" Archived 20130526 at the Wayback Machine quote: "techniques which can reduce the PAPR, ... could result in a significant saving in electricity costs."
 ^ Huleihel, Yara; BenDror, Eilam; Permuter, Haim H. (2020). Low PAPR Waveform Design for OFDM Systems Based on Convolutional Autoencoder. 2020 IEEE International Conference on Advanced Networks and Telecommunications Systems (ANTS). pp. 16.
 ^ "What Is The "Crest Factor" And Why Is It Used?" (PDF). Archived from the original (PDF) on 20110927. Retrieved 20060307.
 ^ Crest factor analysis for complex signal processing Archived 20060427 at the Wayback Machine
 ^ PAPR simulation for 64QAM
 ^ Crest factor definition — AES Pro Audio Reference
 ^ "Level Practices in Digital Audio". Archived from the original on 20090618. Retrieved 20091011.
 ^ Gain Structure — Setting the System Levels Archived 20070928 at the Wayback Machine, Mackie Mixer Tips
 ^ Setting sound system level controls: The most expensive system set up wrong never performs as well as an inexpensive system set up correctly.
 ^ Palatal snoring identified by acoustic crest factor analysis
General
This article incorporates public domain material from Federal Standard 1037C. General Services Administration. Archived from the original on 20220122. (in support of MILSTD188).
External links
 Definition of peaktoaverage ratio – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
 Definition of crest factor – ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
 Peaktoaverage power ratio (PAPR) of OFDM systems  tutorial