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signal processing

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| footer = The signal on the left looks like noise, but the signal processing technique known as the Fourier transform (right) shows that it contains five well defined frequency components.

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| footer = The signal on the left looks like noise, but the signal processing technique known as the Fourier transform (right) shows that it contains five well defined frequency components.

**Signal processing**is an electrical engineering subfield that focuses on analysing, modifying and synthesizing signals such as sound, images and biological measurements.JOURNAL, Sengupta, Nandini, Sahidullah, Md, Saha, Goutam, August 2016, Lung sound classification using cepstral-based statistical features, Computers in Biology and Medicine, 75, 1, 118â€“129, 10.1016/j.compbiomed.2016.05.013, Signal processing techniques can be used to improve transmission, storage efficiency and subjective quality and to also emphasize or detect components of interest in a measured signal.BOOK, Discrete-Time Signal Processing, Alan V. Oppenheim and Ronald W. Schafer, Prentice Hall, 1989, 0-13-216771-9, 1,

## History

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. Oppenheim and Schafer further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s.BOOK, Digital Signal Processing, 1975, Prentice Hall, 0-13-214635-5, Oppenheim, Alan V., Schafer, Ronald W., 5, In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal.WEB,weblink A Mathematical Theory of Communication - CHM Revolution, Computer History, 2019-05-13, The paper laid the groundwork for later development of information communication systems. Around the same time, methods of signal transmission were being rapidly developed, as a new type of signal emerged called*processing signals*.BOOK, Fifty Years of Signal Processing, The IEEE Signal Processing Society, 1998, Electronic signal processing was revolutonized by the MOSFET (metal-oxide-semiconductor field-effect transistor, or MOS transistor),BOOK, Grant, Duncan Andrew, Gowar, John, Power MOSFETS: theory and applications, 1989, Wiley (publisher), Wiley, 9780471828679, 1,weblink The metal-oxide-semiconductor field-effect transistor (MOSFET) is the most commonly used active device in the very large-scale integration of digital integrated circuits (VLSI). During the 1970s these components revolutionized electronic signal processing, control systems and computers., which was originally invented by Mohamed M. Atalla and Dawon Kahng in 1959.WEB,weblink 1960: Metal Oxide Semiconductor (MOS) Transistor Demonstrated, The Silicon Engine: A Timeline of Semiconductors in Computers, Computer History Museum, August 31, 2019, MOS integrated circuit technology was the basis for the first single-chip microprocessors and microcontrollers in the early 1970s,JOURNAL, Shirriff, Ken, The Surprising Story of the First Microprocessors, IEEE Spectrum, 30 August 2016, Institute of Electrical and Electronics Engineers,weblink 13 October 2019, and then the first single-chip digital signal processor (DSP) in 1979.WEB,weblink 1979: Single Chip Digital Signal Processor Introduced, The Silicon Engine, Computer History Museum, 2019-05-13, JOURNAL, DSPs: Back to the Future, ACM Queue, April 16, 2004, 2, 1,weblink 14 October 2019,

## Categories

### Analog

Analog signal processing is for signals that have not been digitized, as in legacy radio, telephone, radar, and television systems. This involves linear electronic circuits as well as non-linear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators and delay lines. Non-linear circuits include compandors, multiplicators (frequency mixers and voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators and phase-locked loops.### Continuous time

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 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.

### Digital

Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and lookup tables. Examples of algorithms are the fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters.### Nonlinear

Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains.BOOK, Billings, S. A., Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, Wiley, 2013, 1119943590, Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods.### Statistical

Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks.BOOK, Louis L., Scharf, Statistical signal processing: detection, estimation, and time series analysis, Addisonâ€“Wesley, Boston, 1991, 0-201-19038-9, 61160161, 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.## Application fields

(File:Seismic Data Processing.jpg|thumb|Seismic signal processing)- Audio signal processing{{spaced ndash}} for electrical signals representing sound, such as speech or music
- Speech signal processing{{spaced ndash}} for processing and interpreting spoken words
- Image processing{{spaced ndash}} in digital cameras, computers and various imaging systems
- Video processing{{spaced ndash}} for interpreting moving pictures
- Wireless communication{{spaced ndash}} waveform generations, demodulation, filtering, equalization
- Control systems
- Array processing{{spaced ndash}} for processing signals from arrays of sensors
- Process control{{spaced ndash}} a variety of signals are used, including the industry standard 4-20 mA current loop
- Seismology
- Financial signal processing{{spaced ndash}} analyzing financial data using signal processing techniques, especially for prediction purposes.
- Feature extraction, such as image understanding and speech recognition.
- Quality improvement, such as noise reduction, image enhancement, and echo cancellation.
- (Source coding), including audio compression, image compression, and video compression.
- Genomics, Genomic signal processingBOOK, D., Anastassiou, Genomic signal processing, 2001, IEEE,weblink

- OSI layer 1 in the seven layer OSI model, the Physical Layer (modulation, equalization, multiplexing, etc.);
- OSI layer 2, the Data Link Layer (Forward Error Correction);
- OSI layer 6, the Presentation Layer (source coding, including analog-to-digital conversion and signal compression).

## Typical devices

- Filters{{spaced ndash}} 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.
- Signal compressors
- Digital signal processors (DSPs)

## Mathematical methods applied

- Differential equationsBOOK, Patrick Gaydecki, Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design,weblink 2004, IET, 978-0-85296-431-6, 40â€“,
- Recurrence relationBOOK, Shlomo Engelberg, Digital Signal Processing: An Experimental Approach,weblink 8 January 2008, Springer Science & Business Media, 978-1-84800-119-0,
- Transform theory
- Time-frequency analysis{{spaced ndash}} for processing non-stationary signalsBOOK, Time frequency signal analysis and processing a comprehensive reference, 2003, Elsevier, Amsterdam, 0-08-044335-4, 1, Boashash, Boualem,
- Spectral estimation{{spaced ndash}} for determining the spectral content (i.e., the distribution of power over frequency) of a time seriesBOOK, Petre, Stoica, Randolph, Moses, Spectral Analysis of Signals, 2005, Prentice Hall, NJ,weblink
- Statistical signal processing{{spaced ndash}} analyzing and extracting information from signals and noise based on their stochastic properties
- Linear time-invariant system theory, and transform theory
- Polynomial signal processing{{spaced ndash}} analysis of systems which relate input and output using polynomials
- System identification and classification
- Calculus
- Complex analysisBOOK, Peter J. Schreier, Louis L. Scharf, Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals,weblink 4 February 2010, Cambridge University Press, 978-1-139-48762-7,
- Vector spaces and Linear algebraBOOK, Max A. Little, Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics,weblink 13 August 2019, OUP Oxford, 978-0-19-102431-3,
- Functional analysisBOOK, Steven B. Damelin, Willard Miller, Jr, The Mathematics of Signal Processing,weblink 2012, Cambridge University Press, 978-1-107-01322-3,
- Probability and stochastic processes
- Detection theory
- Estimation theory
- OptimizationBOOK, Daniel P. Palomar, Yonina C. Eldar, Convex Optimization in Signal Processing and Communications,weblink 2010, Cambridge University Press, 978-0-521-76222-9,
- Numerical methods
- Time series
- Data mining{{spaced ndash}} for statistical analysis of relations between large quantities of variables (in this context representing many physical signals), to extract previously unknown interesting patterns

## See also

- Audio filter
- Bounded variation
- Digital image processing
- Dynamic range compression, companding, limiting, and noise gating
- Information theory
- Non-local means
- Reverberation

## References

{{reflist}}## Further reading

- BOOK, P Stoica, R Moses, Spectral Analysis of Signals, 2005, Prentice Hall, NJ,weblink
- BOOK, Steven M., Kay, Fundamentals of Statistical Signal Processing, Prentice Hall, Upper Saddle River, New Jersey, 1993, 0-13-345711-7, 26504848,
- BOOK, Athanasios, Papoulis, Probability, Random Variables, and Stochastic Processes, 1991, third, McGraw-Hill, 0-07-100870-5,
- Kainam Thomas Wong weblink: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.
- Ali H. Sayed, Adaptive Filters, Wiley, NJ, 2008, {{isbn|978-0-470-25388-5}}.
- Thomas Kailath, Ali H. Sayed, and Babak Hassibi, Linear Estimation, Prentice-Hall, NJ, 2000, {{isbn|978-0-13-022464-4}}.

## External links

- Signal Processing for Communications â€“ free online textbook by Paolo Prandoni and Martin Vetterli (2008)
- Scientists and Engineers Guide to Digital Signal Processing â€“ free online textbook by Stephen Smith
- Signal Processing Techniques for Determining Powerplant Characteristics
- The IEEE Signal Processing Society
- Bio-Medical Signal processing at a Glance
- IPython notebooks for Python for Signal Processing Book

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