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Crest factor is a parameter of a
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any dis ...
, such as
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 ...
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 Direct current (DC) is one-directional electric current, flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor (material), conductor such as a wire, but can also flow throug ...
or a
square wave Square wave may refer to: *Square wave (waveform) A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same ...
. 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 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. When expressed in
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a Power, root-power, and field quantities, power or root-power quantity on a logarithmic scale. Two signals whos ...
s, 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 mathematics, a real number is a number that can be used to measure a continuous one- dimensional quantity such as a duration or temperature. Here, ''continuous'' means that pairs of values can have arbitrarily small differences. Every re ...
, 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 A loudspeaker (commonly referred to as a speaker or, more fully, a speaker system) is a combination of one or more speaker drivers, an enclosure, and electrical connections (possibly including a crossover network). The speaker driver is an ...
testing standards; in this context it is usually expressed in dB. The minimum possible crest factor is 1, 1:1 or 0 dB.


Examples

This table provides values for some normalized
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitude Scale (ratio), scales and of any dis ...
s. All peak magnitudes have been normalized to 1. 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 Constant envelope is achieved when a sinusoidal waveform reaches equilibrium in a specific system. This happens when negative feedback in a control system, such as in radio automatic gain control or when an amplifier reaches steady state. Ste ...
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 A linear amplifier is an electronics, electronic circuit whose output is proportional to its input, but capable of delivering more power (physics), power into a Electrical load, load. The term usually refers to a type of radio-frequency (RF) powe ...
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 In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy-channel coding ...
).
Orthogonal frequency-division multiplexing In telecommunications, orthogonal frequency-division multiplexing (OFDM) is a type of digital transmission used in digital modulation for encoding digital (binary) data on multiple carrier frequencies. OFDM has developed into a popular scheme for ...
(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. 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.


Crest factor reduction methods

Various methods for crest factor reduction exist, such as peak windowing,
noise shaping Noise shaping is a technique typically used in digital audio, Image processing, image, and video processing, usually in combination with dithering, as part of the process of Quantization (signal processing), quantization or Audio bit depth, bit-dep ...
, pulse injection and peak cancellation.


Applications

*
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 ...
— for describing the quality of an AC power waveform *
Vibration Vibration () is a mechanical phenomenon whereby oscillations occur about an equilibrium point. Vibration may be deterministic if the oscillations can be characterised precisely (e.g. the periodic motion of a pendulum), or random if the os ...
analysis — for estimating the amount of impact
wear Wear is the damaging, gradual removal or deformation of material at solid surfaces. Causes of wear can be mechanical (e.g., erosion) or chemical (e.g., corrosion). The study of wear and related processes is referred to as tribology. Wear in ...
in a bearing *
Radio Radio is the technology of communicating using radio waves. Radio waves are electromagnetic waves of frequency between 3  hertz (Hz) and 300  gigahertz (GHz). They are generated by an electronic device called a transmitter connec ...
and
audio Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to: Sound *Audio signal, an electrical representation of sound *Audio frequency, a frequency in the audio spectrum *Digital audio, representation of sound ...
electronics — for estimating the headroom required in a signal chain **
Music Music is the arrangement of sound to create some combination of Musical form, form, harmony, melody, rhythm, or otherwise Musical expression, expressive content. Music is generally agreed to be a cultural universal that is present in all hum ...
has a widely varying crest factor. Typical values for a processed mix are around 4–8 (which corresponds to of headroom, usually involving
audio level compression Dynamic range compression (DRC) or simply compression is an audio signal processing operation that reduces the volume of loud sounds or amplifies quiet sounds, thus reducing or ''compressing'' an audio signal's dynamic range. Compression is c ...
), and 8–10 for an unprocessed recording *
Physiology Physiology (; ) is the science, scientific study of function (biology), functions and mechanism (biology), mechanisms in a life, living system. As a branches of science, subdiscipline of biology, physiology focuses on how organisms, organ syst ...
— for analysing the sound of
snoring Snoring is an abnormal breath sound caused by partially obstructed, turbulent airflow and vibration of tissues in the upper respiratory tract (e.g., uvula, soft palate, base of tongue) which occurs during sleep. It usually happens during in ...
Palatal snoring identified by acoustic crest factor analysis
/ref>


See also

*
Clipping (signal processing) Clipping is a form of distortion that limits a signal once it exceeds a threshold. Clipping may occur when a signal is recorded by a sensor that has constraints on the range of data it can measure, it can occur when a signal is digitized, or it ...
* Form factor (electronics)


References


General


External links

* Definition o
peak-to-average ratio
– ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K * Definition o
crest factor
– ATIS (Alliance for Telecommunications Industry Solutions) Telecom Glossary 2K
Peak-to-average power ratio (PAPR) of OFDM systems - tutorial
{{Waveforms Waveforms