Editing Autocorrelation (section)

==Applications==
Autocorrelation's ability to find repeating patterns in [[data]] yields many applications, including:
* Autocorrelation analysis is used heavily in [[fluorescence correlation spectroscopy]]<ref>{{Cite journal|last=Elson|first=Elliot L.|date=December 2011|title=Fluorescence Correlation Spectroscopy: Past, Present, Future|journal=Biophysical Journal|language=en|volume=101|issue=12|pages=2855–2870|doi=10.1016/j.bpj.2011.11.012|pmc=3244056|pmid=22208184|bibcode=2011BpJ...101.2855E}}</ref> to provide quantitative insight into molecular-level diffusion and chemical reactions.<ref>{{Cite journal|last1=Hołyst|first1=Robert|last2=Poniewierski|first2=Andrzej|last3=Zhang|first3=Xuzhu|date=2017|title=Analytical form of the autocorrelation function for the fluorescence correlation spectroscopy|journal=Soft Matter|language=en|volume=13|issue=6|pages=1267–1275|doi=10.1039/C6SM02643E|pmid=28106203|issn=1744-683X|bibcode=2017SMat...13.1267H|doi-access=free}}</ref>
* Another application of autocorrelation is the measurement of [[optical spectrum|optical spectra]] and the measurement of very-short-duration [[light]] [[ultrashort pulse|pulses]] produced by [[laser]]s, both using [[optical autocorrelation|optical autocorrelators]].
* Autocorrelation is used to analyze [[dynamic light scattering]] data, which notably enables determination of the [[particle size distribution]]s of nanometer-sized particles or [[micelle]]s suspended in a fluid. A laser shining into the mixture produces a [[speckle pattern]] that results from the motion of the particles. Autocorrelation of the signal can be analyzed in terms of the diffusion of the particles. From this, knowing the viscosity of the fluid, the sizes of the particles can be calculated.
* Utilized in the [[GPS]] system to correct for the [[propagation delay]], or time shift, between the point of time at the transmission of the [[carrier signal]] at the satellites, and the point of time at the receiver on the ground.  This is done by the receiver generating a replica signal of the 1,023-bit C/A (Coarse/Acquisition) code, and generating lines of code chips [-1,1] in packets of ten at a time, or 10,230 chips (1,023 × 10), shifting slightly as it goes along in order to accommodate for the [[doppler shift]] in the incoming satellite signal, until the receiver replica signal and the satellite signal codes match up.<ref>{{cite book |last1=Van Sickle |first1=Jan |title=GPS for Land Surveyors |date=2008 |publisher=CRC Press |isbn=978-0-8493-9195-8 |pages=18–19 |edition=Third}}</ref>
* The [[small-angle X-ray scattering]] intensity of a nanostructured system is the Fourier transform of the spatial autocorrelation function of the electron density.
*In [[surface science]] and [[scanning probe microscopy]], autocorrelation is used to establish a link between surface morphology and functional characteristics.<ref>{{Cite journal|last1=Kalvani|first1=Payam Rajabi|last2=Jahangiri|first2=Ali Reza|last3=Shapouri|first3=Samaneh|last4=Sari|first4=Amirhossein|last5=Jalili|first5=Yousef Seyed|date=August 2019|title=Multimode AFM analysis of aluminum-doped zinc oxide thin films sputtered under various substrate temperatures for optoelectronic applications|journal=Superlattices and Microstructures|language=en|volume=132|pages=106173|doi=10.1016/j.spmi.2019.106173|s2cid=198468676 }}</ref>
* In optics, normalized autocorrelations and cross-correlations give the [[degree of coherence]] of an electromagnetic field.
* In [[astronomy]], autocorrelation can determine the [[frequency]] of [[pulsar]]s.
* In [[music]], autocorrelation (when applied at time scales smaller than a second) is used as a [[pitch detection algorithm]] for both instrument tuners and "Auto Tune" (used as a [[Distortion (music)|distortion]] effect or to fix intonation).<ref>{{Cite news
  | last1 = Tyrangiel | first1 = Josh
 | title = Auto-Tune: Why Pop Music Sounds Perfect
 | magazine = [[Time (magazine)|Time]]
 | date = 2009-02-05
 | url = http://www.time.com/time/magazine/article/0,9171,1877372,00.html| archive-url = https://web.archive.org/web/20090210004826/http://www.time.com/time/magazine/article/0,9171,1877372,00.html| url-status = dead| archive-date = February 10, 2009}}</ref> When applied at time scales larger than a second, autocorrelation can identify the [[Beat (music)|musical beat]], for example to determine [[tempo]].
* Autocorrelation in space rather than time, via the [[Patterson function]], is used by X-ray diffractionists to help recover the "Fourier phase information" on atom positions not available through diffraction alone.
* In statistics, spatial autocorrelation between sample locations also helps one estimate [[Variance generalizations|mean value uncertainties]] when sampling a heterogeneous population.
* The [[SEQUEST]] algorithm for analyzing [[Mass spectrum|mass spectra]] makes use of autocorrelation in conjunction with [[cross-correlation]] to score the similarity of an observed spectrum to an idealized spectrum representing a [[peptide]].
* In [[astrophysics]], autocorrelation is used to study and characterize the spatial distribution of [[Galaxy|galaxies]] in the universe and in multi-wavelength observations of low mass [[X-ray binary|X-ray binaries]].
* In [[panel data]], spatial autocorrelation refers to correlation of a variable with itself through space.
* In analysis of [[Markov chain Monte Carlo]] data, autocorrelation must be taken into account for correct error determination.
* In [[geosciences]] (specifically in [[geophysics]]) it can be used to compute an autocorrelation seismic attribute, out of a 3D seismic survey of the underground.
* In [[medical ultrasound]] imaging, autocorrelation is used to visualize blood flow.
* In [[intertemporal portfolio choice]], the presence or absence of autocorrelation in an asset's [[rate of return]] can affect the optimal portion of the portfolio to hold in that asset.
* In [[numerical relay]]s, autocorrelation has been used to accurately measure power system frequency.<ref>{{cite web |url=https://cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6734_NewMethod_BK_20151112_Web.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://cdn.selinc.com/assets/Literature/Publications/Technical%20Papers/6734_NewMethod_BK_20151112_Web.pdf |archive-date=2022-10-09 |url-status=live |title=A New Method for Fast Frequency Measurement for Protection Applications |last=Kasztenny |first=Bogdan |date= March 2016 |publisher=Schweitzer Engineering Laboratories |access-date=28 May 2022}}</ref>