Crest factor

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. This is equivalent to the ratio of the L∞ norm to the L2 norm of the function of the waveform:
The peak-to-average power ratio (PAPR) is the peak amplitude squared (giving the peak "power") divided by the RMS value squared (giving the average "power"). It is the square of the crest factor:
formula_12 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.
Digital multimeters.
Crest factor is an important parameter to understand when trying to take accurate measurements of low frequency signals. For example, given a certain digital multimeter with an AC accuracy of 0.03% (always specified for sine waves) with an additional error of 0.2% for crest factors between 1.414 and 5, then the total error for measuring a triangular wave (crest factor = 1.73) is 0.03% + 0.2% = 0.23%.
Acoustics and audio engineering.
In acoustics and audio engineering, crest factor is usually expressed in decibels, so it's defined as the level difference between the RMS and the peak value of the waveform. For example, for a sine wave the 1.414 ratio is 20 log(1.414) or 3 dB. Most ambient noise has a crest factor of around 10 dB while impulsive sounds such as gunshots can have crest factors of over 30 dB.
Peak-to-average ratio (PAR) meter.
A "peak-to-average ratio meter" ("Par meter") is a device used to measure the ratio of the peak power level to the time-averaged power level in an electrical circuit. This quantity is known as the peak-to-average ratio ("p/a" r or PAR). Such meters are used as a quick means to identify degraded telephone channels.
Par meters are very sensitive to envelope delay distortion. They may also be used for idle channel noise, nonlinear distortion, and amplitude-distortion measurements.
The peak-to-average ratio can be determined for many signal parameters, such as voltage, current, power, frequency, and phase.
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:
Orthogonal frequency-division multiplexing (OFDM) is a very promising modulation technique; perhaps its biggest problem is its high crest factor. Many crest factor reduction techniques (CFR) have been proposed for OFDM. 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 lower-power hardware (and therefore lower electricity costs and less expensive hardware), or both.
Crest factor reduction methods.
Various methods for crest factor reduction exist, such as peak windowing, noise shaping, pulse injection and peak cancellation.