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Digital signal processing

January 20, 2023

"Digital transform" redirects here. For the impact of digital technology on society, see Digital transformation.

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train,[1][2] which is typically generated by the switching of a transistor.[3]

Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others.

DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification[4] and can be implemented in the time, frequency, and spatio-temporal domains.

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.[5] Digital signal processing is also fundamental to digital technology, such as digital telecommunication and wireless communications.[6] DSP is applicable to both streaming data and static (stored) data.

Signal sampling

Main article: Sampling (signal processing)

To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter (ADC).[7] Sampling is usually carried out in two stages, discretization and 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.

The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is often significantly higher than this.[8]

Theoretical DSP analyses and derivations are typically performed on discrete-time signal models with no amplitude inaccuracies (quantization error), "created" by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an ADC. The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a digital-to-analog converter (DAC).

Domains

DSP engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains. They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain representation.

Time and space domains

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.

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. The surrounding samples may be identified with respect to time or space. The output of a linear digital filter to any given input may be calculated by convolving the input signal with an impulse response.

Frequency domain

Main article: Frequency domain

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.

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 filters.

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.

Z-plane analysis

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.

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.[9] Prony's method can be used to estimate phases, amplitudes, initial phases and decays of the components of signal.[10][9] Components are assumed to be complex decaying exponents.[10][9]

Time-frequency analysis

A time-frequency representation of signal can capture both temporal evolution and frequency structure of analyzed signal. Temporal and frequency resolution are limited by the principle of uncertainty and the tradeoff is adjusted by the width of analysis window. Linear techniques such as Short-time Fourier transform, wavelet transform, filter bank,[11] non-linear (e.g., Wigner–Ville transform[10]) and autoregressive methods (e.g. segmented Prony method)[10][12][13] 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[14] are based on windowed spectral analysis.

Wavelet

 
An example of the 2D discrete wavelet transform that is used in JPEG2000. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left.

In numerical analysis and functional analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information. The accuracy of the joint time-frequency resolution is limited by the uncertainty principle of time-frequency.

Empirical mode decomposition

Empirical mode decomposition is based on decomposition signal into intrinsic mode functions (IMFs). IMFs are quasiharmonical oscillations that are extracted from the signal.[15]

Implementation

DSP algorithms may be run on general-purpose computers and digital signal processors. DSP algorithms are also implemented on purpose-built hardware such as application-specific integrated circuit (ASICs). Additional technologies for digital signal processing include more powerful general purpose microprocessors, graphics processing units, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors.[16]

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 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 photographs 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 FPGAs may be used.[17] For the most demanding applications or high-volume products, ASICs might be designed specifically for the application.

Parallel implementations of DSP algorithms, utilising multi-core CPU and many-core GPU architectures, are developed to improve the performances in terms of latency of these algorithms.[18]

Native processing is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional third-party DSP chips located on extension cards or external hardware boxes or racks. Many digital audio workstations such as Logic Pro, Cubase, Digital Performer and Pro Tools LE use native processing. Others, such as Pro Tools HD, Universal Audio's UAD-1 and TC Electronic's Powercore use DSP processing.

Applications

General application areas for DSP include

Specific examples include speech coding and transmission in digital mobile phones, room correction of sound in hi-fi and sound reinforcement applications, analysis and control of industrial processes, medical imaging such as CAT scans and MRI, audio crossovers and equalization, digital synthesizers, and audio effects units.[19]

Techniques

Related fields

Further reading

 
Wikibooks has a book on the topic of: Digital Signal Processing
  • Ahmed, Nasir; Rao, Kamisetty Ramamohan (7 August 1975). Orthogonal Transforms for Digital Signal Processing. New York: Springer-Verlag. doi:10.1109/ICASSP.1976.1170121. ISBN 978-3540065562. LCCN 73018912. OCLC 438821458. OL 22806004M. S2CID 10776771.
  • Jonathan M. Blackledge, Martin Turner: Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications, Horwood Publishing, ISBN 1-898563-48-9
  • James D. Broesch: Digital Signal Processing Demystified, Newnes, ISBN 1-878707-16-7
  • Dyer, Stephen A.; Harms, Brian K. (13 August 1993). "Digital Signal Processing". In Yovits, Marshall C. (ed.). Advances in Computers. Vol. 37. Academic Press. pp. 59–118. doi:10.1016/S0065-2458(08)60403-9. ISBN 978-0120121373. ISSN 0065-2458. LCCN 59015761. OCLC 858439915. OL 10070096M.
  • Paul M. Embree, Damon Danieli: C++ Algorithms for Digital Signal Processing, Prentice Hall, ISBN 0-13-179144-3
  • Hari Krishna Garg: Digital Signal Processing Algorithms, CRC Press, ISBN 0-8493-7178-3
  • P. Gaydecki: Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design, Institution of Electrical Engineers, ISBN 0-85296-431-5
  • Ashfaq Khan: Digital Signal Processing Fundamentals, Charles River Media, ISBN 1-58450-281-9
  • Sen M. Kuo, Woon-Seng Gan: Digital Signal Processors: Architectures, Implementations, and Applications, Prentice Hall, ISBN 0-13-035214-4
  • Paul A. Lynn, Wolfgang Fuerst: Introductory Digital Signal Processing with Computer Applications, John Wiley & Sons, ISBN 0-471-97984-8
  • Richard G. Lyons: Understanding Digital Signal Processing, Prentice Hall, ISBN 0-13-108989-7
  • Vijay Madisetti, Douglas B. Williams: The Digital Signal Processing Handbook, CRC Press, ISBN 0-8493-8572-5
  • James H. McClellan, Ronald W. Schafer, Mark A. Yoder: Signal Processing First, Prentice Hall, ISBN 0-13-090999-8
  • Bernard Mulgrew, Peter Grant, John Thompson: Digital Signal Processing – Concepts and Applications, Palgrave Macmillan, ISBN 0-333-96356-3
  • Boaz Porat: A Course in Digital Signal Processing, Wiley, ISBN 0-471-14961-6
  • John G. Proakis, Dimitris Manolakis: Digital Signal Processing: Principles, Algorithms and Applications, 4th ed, Pearson, April 2006, ISBN 978-0131873742
  • John G. Proakis: A Self-Study Guide for Digital Signal Processing, Prentice Hall, ISBN 0-13-143239-7
  • Charles A. Schuler: Digital Signal Processing: A Hands-On Approach, McGraw-Hill, ISBN 0-07-829744-3
  • Doug Smith: Digital Signal Processing Technology: Essentials of the Communications Revolution, American Radio Relay League, ISBN 0-87259-819-5
  • Smith, Steven W. (2002). Digital Signal Processing: A Practical Guide for Engineers and Scientists. Newnes. ISBN 0-7506-7444-X.
  • Stein, Jonathan Yaakov (2000-10-09). Digital Signal Processing, a Computer Science Perspective. Wiley. ISBN 0-471-29546-9.
  • Stergiopoulos, Stergios (2000). Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems. CRC Press. ISBN 0-8493-3691-0.
  • Van De Vegte, Joyce (2001). Fundamentals of Digital Signal Processing. Prentice Hall. ISBN 0-13-016077-6.
  • Oppenheim, Alan V.; Schafer, Ronald W. (2001). Discrete-Time Signal Processing. Pearson. ISBN 1-292-02572-7.
  • Hayes, Monson H. Statistical digital signal processing and modeling. John Wiley & Sons, 2009. (with MATLAB scripts)

References

  1. ^ B. SOMANATHAN NAIR (2002). Digital electronics and logic design. PHI Learning Pvt. Ltd. p. 289. ISBN 9788120319561. Digital signals are fixed-width pulses, which occupy only one of two levels of amplitude.
  2. ^ Joseph Migga Kizza (2005). Computer Network Security. Springer Science & Business Media. ISBN 9780387204734.
  3. ^ 2000 Solved Problems in Digital Electronics. Tata McGraw-Hill Education. 2005. p. 151. ISBN 978-0-07-058831-8.
  4. ^ Billings, Stephen A. (Sep 2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. UK: Wiley. ISBN 978-1-119-94359-4.
  5. ^ Broesch, James D.; Stranneby, Dag; Walker, William (2008-10-20). Digital Signal Processing: Instant access (1 ed.). Butterworth-Heinemann-Newnes. p. 3. ISBN 9780750689762.
  6. ^ Srivastava, Viranjay M.; Singh, Ghanshyam (2013). MOSFET Technologies for Double-Pole Four-Throw Radio-Frequency Switch. Springer Science & Business Media. p. 1. ISBN 9783319011653.
  7. ^ Walden, R. H. (1999). "Analog-to-digital converter survey and analysis". IEEE Journal on Selected Areas in Communications. 17 (4): 539–550. doi:10.1109/49.761034.
  8. ^ Candes, E. J.; Wakin, M. B. (2008). "An Introduction To Compressive Sampling". IEEE Signal Processing Magazine. 25 (2): 21–30. Bibcode:2008ISPM...25...21C. doi:10.1109/MSP.2007.914731. S2CID 1704522.
  9. ^ a b c Marple, S. Lawrence (1987-01-01). Digital Spectral Analysis: With Applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 978-0-13-214149-9.
  10. ^ a b c d Ribeiro, M.P.; Ewins, D.J.; Robb, D.A. (2003-05-01). "Non-stationary analysis and noise filtering using a technique extended from the original Prony method". Mechanical Systems and Signal Processing. 17 (3): 533–549. Bibcode:2003MSSP...17..533R. doi:10.1006/mssp.2001.1399. ISSN 0888-3270. Retrieved 2019-02-17.
  11. ^ So, Stephen; Paliwal, Kuldip K. (2005). "Improved noise-robustness in distributed speech recognition via perceptually-weighted vector quantisation of filterbank energies". Ninth European Conference on Speech Communication and Technology.
  12. ^ Mitrofanov, Georgy; Priimenko, Viatcheslav (2015-06-01). "Prony Filtering of Seismic Data". Acta Geophysica. 63 (3): 652–678. Bibcode:2015AcGeo..63..652M. doi:10.1515/acgeo-2015-0012. ISSN 1895-6572. S2CID 130300729.
  13. ^ Mitrofanov, Georgy; Smolin, S. N.; Orlov, Yu. A.; Bespechnyy, V. N. (2020). "Prony decomposition and filtering". Geology and Mineral Resources of Siberia (2): 55–67. doi:10.20403/2078-0575-2020-2-55-67. ISSN 2078-0575. S2CID 226638723. Retrieved 2020-09-08.
  14. ^ Gonzalez, Sira; Brookes, Mike (February 2014). "PEFAC - A Pitch Estimation Algorithm Robust to High Levels of Noise". IEEE/ACM Transactions on Audio, Speech, and Language Processing. 22 (2): 518–530. doi:10.1109/TASLP.2013.2295918. ISSN 2329-9290. S2CID 13161793. Retrieved 2017-12-03.
  15. ^ Huang, N. E.; Shen, Z.; Long, S. R.; Wu, M. C.; Shih, H. H.; Zheng, Q.; Yen, N.-C.; Tung, C. C.; Liu, H. H. (1998-03-08). "The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 454 (1971): 903–995. Bibcode:1998RSPSA.454..903H. doi:10.1098/rspa.1998.0193. ISSN 1364-5021. S2CID 1262186. Retrieved 2018-06-05.
  16. ^ Stranneby, Dag; Walker, William (2004). Digital Signal Processing and Applications (2nd ed.). Elsevier. ISBN 0-7506-6344-8.
  17. ^ JPFix (2006). "FPGA-Based Image Processing Accelerator". Retrieved 2008-05-10.
  18. ^ Kapinchev, Konstantin; Bradu, Adrian; Podoleanu, Adrian (December 2019). "Parallel Approaches to Digital Signal Processing Algorithms with Applications in Medical Imaging". 2019 13th International Conference on Signal Processing and Communication Systems (ICSPCS): 1–7. doi:10.1109/ICSPCS47537.2019.9008720. ISBN 978-1-7281-2194-9. S2CID 211686462.
  19. ^ Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, NJ: Prentice-Hall, Inc. ISBN 978-0139141010.

January 20, 2023
digital, signal, processing, digital, transform, redirects, here, impact, digital, technology, society, digital, transformation, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sourc. Digital transform redirects here For the impact of digital technology on society see Digital transformation This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Digital signal processing news newspapers books scholar JSTOR May 2008 Learn how and when to remove this template message Digital signal processing DSP is the use of digital processing such as by computers or more specialized digital signal processors to perform a wide variety of signal processing operations The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time space or frequency In digital electronics a digital signal is represented as a pulse train 1 2 which is typically generated by the switching of a transistor 3 Digital signal processing and analog signal processing are subfields of signal processing DSP applications include audio and speech processing sonar radar and other sensor array processing spectral density estimation statistical signal processing digital image processing data compression video coding audio coding image compression signal processing for telecommunications control systems biomedical engineering and seismology among others DSP can involve linear or nonlinear operations Nonlinear signal processing is closely related to nonlinear system identification 4 and can be implemented in the time frequency and spatio temporal domains 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 5 Digital signal processing is also fundamental to digital technology such as digital telecommunication and wireless communications 6 DSP is applicable to both streaming data and static stored data Contents 1 Signal sampling 2 Domains 2 1 Time and space domains 2 2 Frequency domain 2 3 Z plane analysis 2 4 Autoregression analysis 2 5 Time frequency analysis 2 6 Wavelet 2 7 Empirical mode decomposition 3 Implementation 4 Applications 5 Techniques 6 Related fields 7 Further reading 8 ReferencesSignal sampling EditMain article Sampling signal processing To digitally analyze and manipulate an analog signal it must be digitized with an analog to digital converter ADC 7 Sampling is usually carried out in two stages discretization and 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 The Nyquist Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal In practice the sampling frequency is often significantly higher than this 8 Theoretical DSP analyses and derivations are typically performed on discrete time signal models with no amplitude inaccuracies quantization error created by the abstract process of sampling Numerical methods require a quantized signal such as those produced by an ADC The processed result might be a frequency spectrum or a set of statistics But often it is another quantized signal that is converted back to analog form by a digital to analog converter DAC Domains EditDSP engineers usually study digital signals in one of the following domains time domain one dimensional signals spatial domain multidimensional signals frequency domain and wavelet domains They choose the domain in which to process a signal by making an informed assumption or by trying different possibilities as to which domain best represents the essential characteristics of the signal and the processing to be applied to it A sequence of samples from a measuring device produces a temporal or spatial domain representation whereas a discrete Fourier transform produces the frequency domain representation Time and space domains Edit 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 The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering Digital filtering generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal The surrounding samples may be identified with respect to time or space The output of a linear digital filter to any given input may be calculated by convolving the input signal with an impulse response Frequency domain Edit Main article Frequency domain 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 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 filters 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 Z plane analysis Edit 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 Autoregression analysis Edit 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 9 Prony s method can be used to estimate phases amplitudes initial phases and decays of the components of signal 10 9 Components are assumed to be complex decaying exponents 10 9 Time frequency analysis Edit A time frequency representation of signal can capture both temporal evolution and frequency structure of analyzed signal Temporal and frequency resolution are limited by the principle of uncertainty and the tradeoff is adjusted by the width of analysis window Linear techniques such as Short time Fourier transform wavelet transform filter bank 11 non linear e g Wigner Ville transform 10 and autoregressive methods e g segmented Prony method 10 12 13 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 14 are based on windowed spectral analysis Wavelet Edit An example of the 2D discrete wavelet transform that is used in JPEG2000 The original image is high pass filtered yielding the three large images each describing local changes in brightness details in the original image It is then low pass filtered and downscaled yielding an approximation image this image is high pass filtered to produce the three smaller detail images and low pass filtered to produce the final approximation image in the upper left In numerical analysis and functional analysis a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled As with other wavelet transforms a key advantage it has over Fourier transforms is temporal resolution it captures both frequency and location information The accuracy of the joint time frequency resolution is limited by the uncertainty principle of time frequency Empirical mode decomposition Edit Empirical mode decomposition is based on decomposition signal into intrinsic mode functions IMFs IMFs are quasiharmonical oscillations that are extracted from the signal 15 Implementation EditDSP algorithms may be run on general purpose computers and digital signal processors DSP algorithms are also implemented on purpose built hardware such as application specific integrated circuit ASICs Additional technologies for digital signal processing include more powerful general purpose microprocessors graphics processing units field programmable gate arrays FPGAs digital signal controllers mostly for industrial applications such as motor control and stream processors 16 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 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 photographs 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 FPGAs may be used 17 For the most demanding applications or high volume products ASICs might be designed specifically for the application Parallel implementations of DSP algorithms utilising multi core CPU and many core GPU architectures are developed to improve the performances in terms of latency of these algorithms 18 Native processing is done by the computer s CPU rather than by DSP or outboard processing which is done by additional third party DSP chips located on extension cards or external hardware boxes or racks Many digital audio workstations such as Logic Pro Cubase Digital Performer and Pro Tools LE use native processing Others such as Pro Tools HD Universal Audio s UAD 1 and TC Electronic s Powercore use DSP processing Applications EditGeneral application areas for DSP include Audio signal processing Audio data compression e g MP3 Video data compression Computer graphics Digital image processing Photo manipulation Speech processing Speech recognition Data transmission Radar Sonar Financial signal processing Economic forecasting Seismology Biomedicine Weather forecasting Specific examples include speech coding and transmission in digital mobile phones room correction of sound in hi fi and sound reinforcement applications analysis and control of industrial processes medical imaging such as CAT scans and MRI audio crossovers and equalization digital synthesizers and audio effects units 19 Techniques EditBilinear transform Discrete Fourier transform Discrete time Fourier transform Filter design Goertzel algorithm Least squares spectral analysis LTI system theory Minimum phase s plane Transfer function Z transformRelated fields EditAnalog signal processing Automatic control Computer engineering Computer science Data compression Dataflow programming Discrete cosine transform Electrical engineering Fourier analysis Information theory Machine learning Real time computing Stream processing Telecommunication Time series WaveletFurther reading Edit Wikibooks has a book on the topic of Digital Signal Processing Ahmed Nasir Rao Kamisetty Ramamohan 7 August 1975 Orthogonal Transforms for Digital Signal Processing New York Springer Verlag doi 10 1109 ICASSP 1976 1170121 ISBN 978 3540065562 LCCN 73018912 OCLC 438821458 OL 22806004M S2CID 10776771 Jonathan M Blackledge Martin Turner Digital Signal Processing Mathematical and Computational Methods Software Development and Applications Horwood Publishing ISBN 1 898563 48 9 James D Broesch Digital Signal Processing Demystified Newnes ISBN 1 878707 16 7 Dyer Stephen A Harms Brian K 13 August 1993 Digital Signal Processing In Yovits Marshall C ed Advances in Computers Vol 37 Academic Press pp 59 118 doi 10 1016 S0065 2458 08 60403 9 ISBN 978 0120121373 ISSN 0065 2458 LCCN 59015761 OCLC 858439915 OL 10070096M Paul M Embree Damon Danieli C Algorithms for Digital Signal Processing Prentice Hall ISBN 0 13 179144 3 Hari Krishna Garg Digital Signal Processing Algorithms CRC Press ISBN 0 8493 7178 3 P Gaydecki Foundations Of Digital Signal Processing Theory Algorithms And Hardware Design Institution of Electrical Engineers ISBN 0 85296 431 5 Ashfaq Khan Digital Signal Processing Fundamentals Charles River Media ISBN 1 58450 281 9 Sen M Kuo Woon Seng Gan Digital Signal Processors Architectures Implementations and Applications Prentice Hall ISBN 0 13 035214 4 Paul A Lynn Wolfgang Fuerst Introductory Digital Signal Processing with Computer Applications John Wiley amp Sons ISBN 0 471 97984 8 Richard G Lyons Understanding Digital Signal Processing Prentice Hall ISBN 0 13 108989 7 Vijay Madisetti Douglas B Williams The Digital Signal Processing Handbook CRC Press ISBN 0 8493 8572 5 James H McClellan Ronald W Schafer Mark A Yoder Signal Processing First Prentice Hall ISBN 0 13 090999 8 Bernard Mulgrew Peter Grant John Thompson Digital Signal Processing Concepts and Applications Palgrave Macmillan ISBN 0 333 96356 3 Boaz Porat A Course in Digital Signal Processing Wiley ISBN 0 471 14961 6 John G Proakis Dimitris Manolakis Digital Signal Processing Principles Algorithms and Applications 4th ed Pearson April 2006 ISBN 978 0131873742 John G Proakis A Self Study Guide for Digital Signal Processing Prentice Hall ISBN 0 13 143239 7 Charles A Schuler Digital Signal Processing A Hands On Approach McGraw Hill ISBN 0 07 829744 3 Doug Smith Digital Signal Processing Technology Essentials of the Communications Revolution American Radio Relay League ISBN 0 87259 819 5 Smith Steven W 2002 Digital Signal Processing A Practical Guide for Engineers and Scientists Newnes ISBN 0 7506 7444 X Stein Jonathan Yaakov 2000 10 09 Digital Signal Processing a Computer Science Perspective Wiley ISBN 0 471 29546 9 Stergiopoulos Stergios 2000 Advanced Signal Processing Handbook Theory and Implementation for Radar Sonar and Medical Imaging Real Time Systems CRC Press ISBN 0 8493 3691 0 Van De Vegte Joyce 2001 Fundamentals of Digital Signal Processing Prentice Hall ISBN 0 13 016077 6 Oppenheim Alan V Schafer Ronald W 2001 Discrete Time Signal Processing Pearson ISBN 1 292 02572 7 Hayes Monson H Statistical digital signal processing and modeling John Wiley amp Sons 2009 with MATLAB scripts References Edit B SOMANATHAN NAIR 2002 Digital electronics and logic design PHI Learning Pvt Ltd p 289 ISBN 9788120319561 Digital signals are fixed width pulses which occupy only one of two levels of amplitude Joseph Migga Kizza 2005 Computer Network Security Springer Science amp Business Media ISBN 9780387204734 2000 Solved Problems in Digital Electronics Tata McGraw Hill Education 2005 p 151 ISBN 978 0 07 058831 8 Billings Stephen A Sep 2013 Nonlinear System Identification NARMAX Methods in the Time Frequency and Spatio Temporal Domains UK Wiley ISBN 978 1 119 94359 4 Broesch James D Stranneby Dag Walker William 2008 10 20 Digital Signal Processing Instant access 1 ed Butterworth Heinemann Newnes p 3 ISBN 9780750689762 Srivastava Viranjay M Singh Ghanshyam 2013 MOSFET Technologies for Double Pole Four Throw Radio Frequency Switch Springer Science amp Business Media p 1 ISBN 9783319011653 Walden R H 1999 Analog to digital converter survey and analysis IEEE Journal on Selected Areas in Communications 17 4 539 550 doi 10 1109 49 761034 Candes E J Wakin M B 2008 An Introduction To Compressive Sampling IEEE Signal Processing Magazine 25 2 21 30 Bibcode 2008ISPM 25 21C doi 10 1109 MSP 2007 914731 S2CID 1704522 a b c Marple S Lawrence 1987 01 01 Digital Spectral Analysis With Applications Englewood Cliffs N J Prentice Hall ISBN 978 0 13 214149 9 a 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