Digital signal processing: Difference between revisions

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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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===Autoregression analysis===

A signal is represented as linear combination of its previous samples. Coefficients of the combination are called autoregression coefficients. This method has higher frequency resolution and can process shorter signals compared to the Fourier transform.<ref name = "Marple">{{Cite book| publisher = Prentice Hall| isbn = 978-0-13-214149-9| last = Marple| first = S. Lawrence| title = Digital Spectral Analysis: With Applications| ___location = Englewood Cliffs, N.J| date = 1987-01-01}}</ref> [[Prony's method]] can be used to estimate phases, amplitudes, initial phases and decays of the components of signal.<ref name = "Ribeiro" /><ref name = "Marple" /> Components are assumed to be complex decaying exponents.<ref name = "Ribeiro">{{Cite journal| doi = 10.1006/mssp.2001.1399| issn = 0888-3270| volume = 17| issue = 3| pages = 533–549| last1 = Ribeiro| first1 = M.P.| last2 = Ewins| first2 = D.J.| last3 = Robb| first3 = D.A.| title = Non-stationary analysis and noise filtering using a technique extended from the original Prony method| journal = Mechanical Systems and Signal Processing| access-date = 2019-02-17| date = 2003-05-01| bibcode = 2003MSSP...17..533R| url = http://linkinghub.elsevier.com/retrieve/pii/S0888327001913998| url-access = subscription}}</ref><ref name = "Marple" />

===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 principle of [[uncertainty principle]] 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| url-access = subscription}}</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| s2cidbibcode = 131617932014ITASL..22..518G| urls2cid = https://ieeexplore.ieee.org/document/670133413161793}}</ref> are based on windowed spectral analysis.

===Wavelet===

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== Implementation ==

DSP [[algorithm]]s may be run on general-purpose computers<ref>{{Cite book |last1=Weipeng |first1=Jiang |last2=Zhiqiang |first2=He |last3=Ran |first3=Duan |last4=Xinglin |first4=Wang |title=7th International Conference on Communications and Networking in China |chapter=Major optimization methods for TD-LTE signal processing based on general purpose processor |date=August 2012 |chapter-url=https://ieeexplore.ieee.org/document/6417593 |pages=797–801 |doi=10.1109/ChinaCom.2012.6417593|isbn=978-1-4673-2699-5 |s2cid=17594911 }}</ref> and [[digital signal processor]]s.<ref>{{Cite book |last1=Zaynidinov |first1=Hakimjon |last2=Ibragimov |first2=Sanjarbek |last3=Tojiboyev |first3=Gayrat |last4=Nurmurodov |first4=Javohir |chapter=Efficiency of Parallelization of Haar Fast Transform Algorithm in Dual-Core Digital Signal Processors |date=2021-06-22 |title=2021 8th International Conference on Computer and Communication Engineering (ICCCE) |url=https://ieeexplore.ieee.org/document/9467190 |publisher=IEEE |pages=7–12 |doi=10.1109/ICCCE50029.2021.9467190 |isbn=978-1-7281-1065-3|s2cid=236187914 }}</ref> DSP algorithms are also implemented on purpose-built hardware such as [[application-specific integrated circuit]] (ASICs).<ref>{{Cite journal |last=Lyakhov |first=P.A. |date=June 2023 |title=Area-Efficient digital filtering based on truncated multiply-accumulate units in residue number system 2 n - 1 , 2 n , 2 n + 1 |journal=Journal of King Saud University - Computer and Information Sciences |language=en |volume=35 |issue=6 |pagesarticle-number=101574 |doi=10.1016/j.jksuci.2023.101574|doi-access=free }}</ref> Additional technologies for digital signal processing include more powerful general-purpose [[microprocessor]]s, [[graphics processing unit]]s, [[field-programmable gate array]]s (FPGAs), [[digital signal controller]]s (mostly for industrial applications such as motor control), and [[stream processing|stream processors]].<ref>{{cite book |title=Digital Signal Processing and Applications |last1=Stranneby |first1=Dag |last2=Walker |first2=William |edition=2nd |publisher=Elsevier |year=2004 |isbn=0-7506-6344-8 |url=https://books.google.com/books?id=NKK1DdqcDVUC&pg=PA241}}</ref>

For systems that do not have a [[real-time computing]] requirement and the signal data (either input or output) exists in data files, processing may be done economically with a general-purpose computer. This is essentially no different from any other [[data processing]], except DSP mathematical techniques (such as the [[Discrete cosine transform|DCT]] and [[FFT]]) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. An example of such an application is processing [[digital photograph]]s with software such as [[Photoshop]].

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{{Div col end}}

Specific examples include [[speech coding]] and transmission in digital [[mobile phone]]s, [[room correction]] of sound in [[hi-fi]] and [[sound reinforcement]] applications, analysis and control of [[industrial process]]es, [[medical imaging]] such as [[Computed axial tomography|CAT]] scans and [[MRI]], [[audio crossover]]s and [[equalization (audio)|equalization]], [[digital synthesizer]]s, and audio [[effects unit]]s.<ref>{{cite book |last1=Rabiner |first1=Lawrence R. |author1-link=Lawrence Rabiner |last2=Gold |first2=Bernard |date=1975 |title=Theory and application of digital signal processing |___location=Englewood Cliffs, NJ |publisher=Prentice-Hall, Inc. |isbn=978-0139141010 |url-access=registration |url=https://archive.org/details/theoryapplicatio00rabi }}</ref> DSP has been used in [[hearing aid]] technology since 1996, which allows for automatic directional microphones, complex digital [[noise reduction]], and improved adjustment of the [[frequency response]].<ref>{{Cite journal |lastlast1=Kerckhoff |firstfirst1=Jessica |last2=Listenberger |first2=Jennifer |last3=Valente |first3=Michael |date=October 1, 2008 |title=Advances in hearing aid technology |url=https://digitalcommons.wustl.edu/audio_hapubs/28 |journal=Contemporary Issues in Communication Science and Disorders |volume=35 |pages=102–112 |doi=10.1044/cicsd_35_F_102}}</ref>

== Techniques ==