The signal on the left looks like noise, but the signal processing technique known as spectral density estimation (right) shows that it contains five well-defined frequency components.
According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.[3]
Continuous-time signal processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points).
The methods of signal processing include time domain, frequency domain, and complex frequency domain. This technology mainly discusses the modeling of a linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals
Discrete time
Discrete-time signal processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.
Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.
The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.
Polynomial signal processing is a type of non-linear signal processing, where polynomial systems may be interpreted as conceptually straightforward extensions of linear systems to the non-linear case.[9]
Statistical
Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.[10] Statistical techniques are widely used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, and construct techniques based on this model to reduce the noise in the resulting image.
In geophysics, signal processing is used to amplify the signal vs the noise within time-series measurements of geophysical data. Processing is conducted within either the time domain or frequency domain, or both.[13][14]
In communication systems, signal processing may occur at:
Filters – for example analog (passive or active) or digital (FIR, IIR, frequency domain or stochastic filters, etc.)
Samplers and analog-to-digital converters for signal acquisition and reconstruction, which involves measuring a physical signal, storing or transferring it as digital signal, and possibly later rebuilding the original signal or an approximation thereof.
Data mining – for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns
^Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features". Computers in Biology and Medicine. 75 (1): 118–129. doi:10.1016/j.compbiomed.2016.05.013. PMID 27286184.
^Alan V. Oppenheim and Ronald W. Schafer (1989). Discrete-Time Signal Processing. Prentice Hall. p. 1. ISBN 0-13-216771-9.
^Oppenheim, Alan V.; Schafer, Ronald W. (1975). Digital Signal Processing. Prentice Hall. p. 5. ISBN 0-13-214635-5.
^"A Mathematical Theory of Communication – CHM Revolution". Computer History. Retrieved 2019-05-13.
^ a bFifty Years of Signal Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998 (PDF). The IEEE Signal Processing Society. 1998.
^Berber, S. (2021). Discrete Communication Systems. United Kingdom: Oxford University Press., page 9, https://books.google.com/books?id=CCs0EAAAQBAJ&pg=PA9
^ a bBillings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley. ISBN 978-1-119-94359-4.
^Slawinska, J.; Ourmazd, A.; Giannakis, D. (2018). "A New Approach to Signal Processing of Spatiotemporal Data". 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE Xplore. pp. 338–342. doi:10.1109/SSP.2018.8450704. ISBN 978-1-5386-1571-3. S2CID 52153144.
^V. John Mathews; Giovanni L. Sicuranza (May 2000). Polynomial Signal Processing. Wiley. ISBN 978-0-471-03414-8.
^ a bScharf, Louis L. (1991). Statistical signal processing: detection, estimation, and time series analysis. Boston: Addison–Wesley. ISBN 0-201-19038-9. OCLC 61160161.
^Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification". Digital Signal Processing. 104: 102795. arXiv:2007.10729. Bibcode:2020DSP...10402795S. doi:10.1016/j.dsp.2020.102795. S2CID 220665533.
^Anastassiou, D. (2001). "Genomic signal processing". IEEE Signal Processing Magazine. 18 (4). IEEE: 8–20. Bibcode:2001ISPM...18....8A. doi:10.1109/79.939833.
^Patrick Gaydecki (2004). Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design. IET. pp. 40–. ISBN 978-0-85296-431-6.
^Shlomo Engelberg (8 January 2008). Digital Signal Processing: An Experimental Approach. Springer Science & Business Media. ISBN 978-1-84800-119-0.
^Boashash, Boualem, ed. (2003). Time frequency signal analysis and processing a comprehensive reference (1 ed.). Amsterdam: Elsevier. ISBN 0-08-044335-4.
^Peter J. Schreier; Louis L. Scharf (4 February 2010). Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals. Cambridge University Press. ISBN 978-1-139-48762-7.
^Max A. Little (13 August 2019). Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics. OUP Oxford. ISBN 978-0-19-102431-3.
^Steven B. Damelin; Willard Miller, Jr (2012). The Mathematics of Signal Processing. Cambridge University Press. ISBN 978-1-107-01322-3.
^Daniel P. Palomar; Yonina C. Eldar (2010). Convex Optimization in Signal Processing and Communications. Cambridge University Press. ISBN 978-0-521-76222-9.
Further reading
P Stoica, R Moses (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.