Digital signal processing: Difference between revisions

The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as [[error detection and correction]] in transmission as well as [[data compression]].<ref>{{cite book |title=Digital Signal Processing: Instant access |last1=Broesch |first1=James D. |last2=Stranneby |first2=Dag |last3=Walker |first3=William |date=2008-10-20 |publisher=Butterworth-Heinemann-Newnes |edition=1 |isbn=9780750689762 |page=3}}</ref> Digital signal processing is also fundamental to [[digital electronics|digital technology]], such as [[digital telecommunication]] and [[wireless communications]].<ref name="Srivastava">{{cite book |last1=Srivastava |first1=Viranjay M. |last2=Singh |first2=Ghanshyam |title=MOSFET Technologies for Double-Pole Four-Throw Radio-Frequency Switch |date=2013 |publisher=[[Springer Science & Business Media]] |isbn=9783319011653 |page=1 |url=https://books.google.com/books?id=fkO9BAAAQBAJ&pg=PA1}}</ref> DSP is applicable to both [[streaming data]] and static (stored) data.

To digitally analyze and manipulate an analog signal, it must be digitized with an [[analog-to-digital converter]] (ADC).<ref>{{cite journal |last=Walden |first=R. H. |date=1999 |title=Analog-to-digital converter survey and analysis |journal=IEEE Journal on Selected Areas in Communications |volume=17 |issue=4 |pages=539–550 |doi=10.1109/49.761034}}</ref> Sampling is usually carried out in two stages, [[discretization]] and [[Quantization (signal processing)|quantization]]. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude.  Quantization means each amplitude measurement is approximated by a value from a finite set.  Rounding [[real numbers]] to integers is an example.

[[Time domain]] refers to the analysis of signals with respect to time. Similarly, space domain refers to the analysis of signals with respect to position, e.g., pixel location for the case of image processing.

Signals are converted from time or space domain to the frequency domain usually through use of the [[Fourier transform]]. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant, often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.

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.

Digital filters come in both [[infinite impulse response]] (IIR) and [[finite impulse response]] (FIR) types. Whereas FIR filters are always stable, IIR filters have feedback loops that may become unstable and oscillate. The [[Z-transform]] provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the [[Laplace transform]], which is used to design and analyze analog IIR filters.

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}}</ref><ref name = "Marple" />

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}}</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.

Empirical mode decomposition is based on decomposition signal into [[intrinsic mode function]]s (IMFs). IMFs are quasi-harmonical oscillations that are extracted from the signal.<ref>{{Cite journal| doi = 10.1098/rspa.1998.0193| issn = 1364-5021| volume = 454| issue = 1971| pages = 903–995| last1 = Huang| first1 = N. E.| last2 = Shen| first2 = Z.| last3 = Long| first3 = S. R.| last4 = Wu| first4 = M. C.| last5 = Shih| first5 = H. H.| last6 = Zheng| first6 = Q.| last7 = Yen| first7 = N.-C.| last8 = Tung| first8 = C. C.| last9 = Liu| first9 = H. H.| title = The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis| journal = Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences| access-date = 2018-06-05| date = 1998-03-08| bibcode = 1998RSPSA.454..903H| s2cid = 1262186| url = http://rspa.royalsocietypublishing.org/cgi/doi/10.1098/rspa.1998.0193}}</ref>

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 |pages=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]].

When the application requirement is real-time, DSP is often implemented using specialized or dedicated processors or microprocessors, sometimes using multiple processors or multiple processing cores. These may process data using fixed-point arithmetic or floating point. For more demanding applications [[FPGA]]s may be used.<ref>{{cite web |last=JPFix |title=FPGA-Based Image Processing Accelerator |url=http://www.jpfix.com/About_Us/Articles/FPGA-Based_Image_Processing_Ac/fpga-based_image_processing_ac.html |date=2006 |access-date=2008-05-10}}</ref> For the most demanding applications or high-volume products, [[ASIC]]s might be designed specifically for the application.

Parallel implementations of DSP algorithms, utilizing multi-core CPU and many-core GPU architectures, are developed to improve the performances in terms of latency of these algorithms.<ref name=":0">{{Cite book |last1=Kapinchev |first1=Konstantin |last2=Bradu |first2=Adrian |last3=Podoleanu |first3=Adrian |title=2019 13th International Conference on Signal Processing and Communication Systems (ICSPCS) |chapter=Parallel Approaches to Digital Signal Processing Algorithms with Applications in Medical Imaging |date=December 2019 |chapter-url=https://ieeexplore.ieee.org/document/9008720 |pages=1–7 |doi=10.1109/ICSPCS47537.2019.9008720|isbn=978-1-7281-2194-9 |s2cid=211686462 |url=https://kar.kent.ac.uk/80930/1/Kapinchev2019.pdf }}</ref>

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 |last=Kerckhoff |first=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>

*{{ cite book | editor-last1 = Yovits | editor-first1 = Marshall C. | last1 = Dyer | first1 = Stephen A. | last2 = Harms | first2 = Brian K. | chapter = Digital Signal Processing | title = Advances in Computers | date = 1993-08-13 | volume = 37 | pages = 59{{hyphen}}118 | publisher = [[Academic Press]] | doi = 10.1016/S0065-2458(08)60403-9 | isbn = 978-0120121373 | issn = 0065-2458 | lccn = 59015761 | chapter-url = https://books.google.com/books?id=vL-bB7GALAwC&pg=PA104 | ol = OL10070096M | oclc = 858439915 | df = dmy-all}}

*{{cite book|url=http://www.dspguide.com|title=Digital Signal Processing: A Practical Guide for Engineers and Scientists|last=Smith|first=Steven W.|date=2002|publisher=Newnes|isbn=0-7506-7444-X}}