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 spatiotemporal 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.
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Digital Signal Processing 1: Basic Concepts and Algorithms Full Course Quiz Solutions
Transcription
Signal sampling
To digitally analyze and manipulate an analog signal, it must be digitized with an analogtodigital 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]} It is common to use an antialiasing filter to limit the signal bandwidth to comply with the sampling theorem, however careful selection of this filter is required because the reconstructed signal will be the filtered signal plus residual aliasing from imperfect stop band rejection instead of the original (unfiltered) signal.
Theoretical DSP analyses and derivations are typically performed on discretetime 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 digitaltoanalog converter (DAC).
Domains
DSP engineers usually study digital signals in one of the following domains: time domain (onedimensional 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
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 nonrealtime 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.
Zplane 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 Ztransform 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]}
Timefrequency analysis
A timefrequency 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 Shorttime Fourier transform, wavelet transform, filter bank,^{[11]} nonlinear (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 timefrequency plane. Nonlinear and segmented Prony methods can provide higher resolution, but may produce undesirable artifacts. Timefrequency analysis is usually used for analysis of nonstationary signals. For example, methods of fundamental frequency estimation, such as RAPT and PEFAC^{[14]} are based on windowed spectral analysis.
Wavelet
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 timefrequency resolution is limited by the uncertainty principle of timefrequency.
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 generalpurpose computers^{[16]} and digital signal processors.^{[17]} DSP algorithms are also implemented on purposebuilt hardware such as applicationspecific integrated circuit (ASICs).^{[18]} Additional technologies for digital signal processing include more powerful general purpose microprocessors, graphics processing units, fieldprogrammable gate arrays (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors.^{[19]}
For systems that do not have a realtime computing requirement and the signal data (either input or output) exists in data files, processing may be done economically with a generalpurpose 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 realtime, DSP is often implemented using specialized or dedicated processors or microprocessors, sometimes using multiple processors or multiple processing cores. These may process data using fixedpoint arithmetic or floating point. For more demanding applications FPGAs may be used.^{[20]} For the most demanding applications or highvolume products, ASICs might be designed specifically for the application.
Parallel implementations of DSP algorithms, utilising multicore CPU and manycore GPU architectures, are developed to improve the performances in terms of latency of these algorithms.^{[21]}
Native processing is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional thirdparty 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 UAD1 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 hifi 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.^{[22]} 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.^{[23]}
Techniques
Related fields
Further reading
 Ahmed, Nasir; Rao, Kamisetty Ramamohan (7 August 1975). "Orthogonal transforms for digital signal processing". ICASSP '76. IEEE International Conference on Acoustics, Speech, and Signal Processing. Vol. 1. New York: SpringerVerlag. pp. 136–140. doi:10.1109/ICASSP.1976.1170121. ISBN 9783540065562. 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 1898563489
 James D. Broesch: Digital Signal Processing Demystified, Newnes, ISBN 1878707167
 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/S00652458(08)604039. ISBN 9780120121373. ISSN 00652458. LCCN 59015761. OCLC 858439915. OL 10070096M.
 Paul M. Embree, Damon Danieli: C++ Algorithms for Digital Signal Processing, Prentice Hall, ISBN 0131791443
 Hari Krishna Garg: Digital Signal Processing Algorithms, CRC Press, ISBN 0849371783
 P. Gaydecki: Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design, Institution of Electrical Engineers, ISBN 0852964315
 Ashfaq Khan: Digital Signal Processing Fundamentals, Charles River Media, ISBN 1584502819
 Sen M. Kuo, WoonSeng Gan: Digital Signal Processors: Architectures, Implementations, and Applications, Prentice Hall, ISBN 0130352144
 Paul A. Lynn, Wolfgang Fuerst: Introductory Digital Signal Processing with Computer Applications, John Wiley & Sons, ISBN 0471979848
 Richard G. Lyons: Understanding Digital Signal Processing, Prentice Hall, ISBN 0131089897
 Vijay Madisetti, Douglas B. Williams: The Digital Signal Processing Handbook, CRC Press, ISBN 0849385725
 James H. McClellan, Ronald W. Schafer, Mark A. Yoder: Signal Processing First, Prentice Hall, ISBN 0130909998
 Bernard Mulgrew, Peter Grant, John Thompson: Digital Signal Processing – Concepts and Applications, Palgrave Macmillan, ISBN 0333963563
 Boaz Porat: A Course in Digital Signal Processing, Wiley, ISBN 0471149616
 John G. Proakis, Dimitris Manolakis: Digital Signal Processing: Principles, Algorithms and Applications, 4th ed, Pearson, April 2006, ISBN 9780131873742
 John G. Proakis: A SelfStudy Guide for Digital Signal Processing, Prentice Hall, ISBN 0131432397
 Charles A. Schuler: Digital Signal Processing: A HandsOn Approach, McGrawHill, ISBN 0078297443
 Doug Smith: Digital Signal Processing Technology: Essentials of the Communications Revolution, American Radio Relay League, ISBN 0872598195
 Smith, Steven W. (2002). Digital Signal Processing: A Practical Guide for Engineers and Scientists. Newnes. ISBN 075067444X.
 Stein, Jonathan Yaakov (20001009). Digital Signal Processing, a Computer Science Perspective. Wiley. ISBN 0471295469.
 Stergiopoulos, Stergios (2000). Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging RealTime Systems. CRC Press. ISBN 0849336910.
 Van De Vegte, Joyce (2001). Fundamentals of Digital Signal Processing. Prentice Hall. ISBN 0130160776.
 Oppenheim, Alan V.; Schafer, Ronald W. (2001). DiscreteTime Signal Processing. Pearson. ISBN 1292025727.
 Hayes, Monson H. Statistical digital signal processing and modeling. John Wiley & Sons, 2009. (with MATLAB scripts)
References
 ^ B. SOMANATHAN NAIR (2002). Digital electronics and logic design. PHI Learning Pvt. Ltd. p. 289. ISBN 9788120319561.
Digital signals are fixedwidth pulses, which occupy only one of two levels of amplitude.
 ^ Joseph Migga Kizza (2005). Computer Network Security. Springer Science & Business Media. ISBN 9780387204734.
 ^ 2000 Solved Problems in Digital Electronics. Tata McGrawHill Education. 2005. p. 151. ISBN 9780070588318.
 ^ Billings, Stephen A. (Sep 2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and SpatioTemporal Domains. UK: Wiley. ISBN 9781119943594.
 ^ Broesch, James D.; Stranneby, Dag; Walker, William (20081020). Digital Signal Processing: Instant access (1 ed.). ButterworthHeinemannNewnes. p. 3. ISBN 9780750689762.
 ^ Srivastava, Viranjay M.; Singh, Ghanshyam (2013). MOSFET Technologies for DoublePole FourThrow RadioFrequency Switch. Springer Science & Business Media. p. 1. ISBN 9783319011653.
 ^ Walden, R. H. (1999). "Analogtodigital 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 (19870101). Digital Spectral Analysis: With Applications. Englewood Cliffs, N.J: Prentice Hall. ISBN 9780132141499.
 ^ ^{a} ^{b} ^{c} ^{d} Ribeiro, M.P.; Ewins, D.J.; Robb, D.A. (20030501). "Nonstationary 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 08883270. Retrieved 20190217.
 ^ So, Stephen; Paliwal, Kuldip K. (2005). "Improved noiserobustness in distributed speech recognition via perceptuallyweighted vector quantisation of filterbank energies". Ninth European Conference on Speech Communication and Technology.
 ^ Mitrofanov, Georgy; Priimenko, Viatcheslav (20150601). "Prony Filtering of Seismic Data". Acta Geophysica. 63 (3): 652–678. Bibcode:2015AcGeo..63..652M. doi:10.1515/acgeo20150012. ISSN 18956572. S2CID 130300729.
 ^ 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:10.20403/20780575202025567. ISSN 20780575. S2CID 226638723. Retrieved 20200908.
 ^ 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 23299290. S2CID 13161793. Retrieved 20171203.
 ^ 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. (19980308). "The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary 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 13645021. S2CID 1262186. Retrieved 20180605.
 ^ Weipeng, Jiang; Zhiqiang, He; Ran, Duan; Xinglin, Wang (August 2012). "Major optimization methods for TDLTE signal processing based on general purpose processor". 7th International Conference on Communications and Networking in China. pp. 797–801. doi:10.1109/ChinaCom.2012.6417593. ISBN 9781467326995. S2CID 17594911.
 ^ Zaynidinov, Hakimjon; Ibragimov, Sanjarbek; Tojiboyev, Gayrat; Nurmurodov, Javohir (20210622). "Efficiency of Parallelization of Haar Fast Transform Algorithm in DualCore Digital Signal Processors". 2021 8th International Conference on Computer and Communication Engineering (ICCCE). IEEE. pp. 7–12. doi:10.1109/ICCCE50029.2021.9467190. ISBN 9781728110653. S2CID 236187914.
 ^ Lyakhov, P.A. (June 2023). "AreaEfficient digital filtering based on truncated multiplyaccumulate units in residue number system 2 n  1 , 2 n , 2 n + 1". Journal of King Saud University  Computer and Information Sciences. 35 (6): 101574. doi:10.1016/j.jksuci.2023.101574.
 ^ Stranneby, Dag; Walker, William (2004). Digital Signal Processing and Applications (2nd ed.). Elsevier. ISBN 0750663448.
 ^ JPFix (2006). "FPGABased Image Processing Accelerator". Retrieved 20080510.
 ^ 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) (PDF). pp. 1–7. doi:10.1109/ICSPCS47537.2019.9008720. ISBN 9781728121949. S2CID 211686462.
 ^ Rabiner, Lawrence R.; Gold, Bernard (1975). Theory and application of digital signal processing. Englewood Cliffs, NJ: PrenticeHall, Inc. ISBN 9780139141010.
 ^ Kerckhoff, Jessica; Listenberger, Jennifer; Valente, Michael (October 1, 2008). "Advances in hearing aid technology". Contemporary Issues in Communication Science and Disorders. 35: 102–112. doi:10.1044/cicsd_35_F_102.