Digital signal processing: Difference between revisions

Revision as of 03:45, 11 August 2025

Latest revision as of 15:19, 25 August 2025

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===Time-frequency analysis===

A time-frequency representation of a signal can capture both temporal evolution and frequency structure of the signal. Temporal and frequency resolution are limited by the [[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 = 13161793| url = https://ieeexplore2014ITASL.ieee.org/document/670133422..518G| url-accesss2cid = subscription13161793}}</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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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 ==