The most common purpose for analysis of signals in the frequency ___domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. Frequency ___domain analysis is also called ''spectrum-'' or ''spectral analysis''.
Filtering, particularly in non-realtime work, can also be achieved in the frequency ___domain, applying the filter and then converting back to the time ___domain. This can be an efficient implementation and can give essentially any filter response, including excellent approximations to [[brickwall filter]]s.
There are some commonly used frequency ___domain transformations. For example, the [[cepstrum]] converts a signal to the frequency ___domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the harmonic structure of the original spectrum.
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===Time-frequency analysis===
A time-frequency representation of a signal can capture both temporal evolution and frequency structure of analyzedthe signal. Temporal and frequency resolution are limited by the [[uncertainty principle of uncertainty]] and the tradeoff is adjusted by the width of the analysis window. Linear techniques such as [[Short-time Fourier transform]], [[wavelet transform]], [[filter bank]],<ref>{{Cite conference| last1 = So| first1 = Stephen| last2 = Paliwal| first2 = Kuldip K.| title = Improved noise-robustness in distributed speech recognition via perceptually-weighted vector quantisation of filterbank energies| book-title = Ninth European Conference on Speech Communication and Technology| date = 2005}}</ref> non-linear (e.g., [[Wigner–Ville transform]]<ref name = "Ribeiro" />) and [[autoregressive]] methods (e.g. segmented Prony method)<ref name = "Ribeiro" /><ref>{{Cite journal| doi = 10.1515/acgeo-2015-0012| issn = 1895-6572| volume = 63| issue = 3| pages = 652–678| last1 = Mitrofanov| first1 = Georgy| last2 = Priimenko| first2 = Viatcheslav| title = Prony Filtering of Seismic Data| journal = Acta Geophysica| date = 2015-06-01| bibcode = 2015AcGeo..63..652M| s2cid = 130300729| doi-access = free}}</ref><ref>{{Cite journal| doi = 10.20403/2078-0575-2020-2-55-67| issn = 2078-0575| issue = 2| pages = 55–67| last1 = Mitrofanov| first1 = Georgy| last2 = Smolin| first2 = S. N.| last3 = Orlov| first3 = Yu. A.| last4 = Bespechnyy| first4 = V. N.| title = Prony decomposition and filtering| journal = Geology and Mineral Resources of Siberia| access-date = 2020-09-08| date = 2020| s2cid = 226638723| url = http://www.jourgimss.ru/en/SitePages/catalog/2020/02/abstract/2020_2_55.aspx}}</ref> are used for representation of signal on the time-frequency plane. Non-linear and segmented Prony methods can provide higher resolution, but may produce undesirable artifacts. Time-frequency analysis is usually used for analysis of non-stationary signals. For example, methods of [[fundamental frequency]] estimation, such as RAPT and PEFAC<ref>{{Cite journal| doi = 10.1109/TASLP.2013.2295918| issn = 2329-9290| volume = 22| issue = 2| pages = 518–530| last1 = Gonzalez| first1 = Sira| last2 = Brookes| first2 = Mike| title = PEFAC - A Pitch Estimation Algorithm Robust to High Levels of Noise| journal = IEEE/ACM Transactions on Audio, Speech, and Language Processing| access-date = 2017-12-03| date = February 2014| s2cid = 13161793| url = https://ieeexplore.ieee.org/document/6701334}}</ref> are based on windowed spectral analysis.
