Signal processing

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.^[1] 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.^[2]

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.^[3]

In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal.^[4] 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.^[5]

Electronic signal processing was revolutionized by the MOSFET (metal-oxide-semiconductor field-effect transistor, or MOS transistor),^[6] which was originally invented by Mohamed M. Atalla and Dawon Kahng in 1959.^[7] MOS integrated circuit technology was the basis for the first single-chip microprocessors and microcontrollers in the early 1970s,^[8] and then the first single-chip digital signal processor (DSP) in 1979.^[9]^[10]

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.^[11] 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.^[12] 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

Audio signal processing – for electrical signals representing sound, such as speech or music
Speech signal processing – for processing and interpreting spoken words
Image processing – in digital cameras, computers and various imaging systems
Video processing – for interpreting moving pictures
Wireless communication – waveform generations, demodulation, filtering, equalization
Control systems
Array processing – for processing signals from arrays of sensors
Process control – a variety of signals are used, including the industry standard 4-20 mA current loop
Seismology
Financial signal processing – 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 processing^[13]

In communication systems, signal processing may occur at:

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 – 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 equations^[14]
Recurrence relation^[15]
Transform theory
Time-frequency analysis – for processing non-stationary signals^[16]
Spectral estimation – for determining the spectral content (i.e., the distribution of power over frequency) of a time series^[17]
Statistical signal processing – analyzing and extracting information from signals and noise based on their stochastic properties
Linear time-invariant system theory, and transform theory
Polynomial signal processing – analysis of systems which relate input and output using polynomials
System identification^[11] and classification
Calculus
Complex analysis^[18]
Vector spaces and Linear algebra^[19]
Functional analysis^[20]
Probability and stochastic processes^[12]
Detection theory
Estimation theory
Optimization^[21]
Numerical methods
Time series
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

References

^ 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.
^ Fifty Years of Signal Processing. The IEEE Signal Processing Society. 1998.
^ Grant, Duncan Andrew; Gowar, John (1989). Power MOSFETS: theory and applications. Wiley. p. 1. ISBN 9780471828679. 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.
^ "1960: Metal Oxide Semiconductor (MOS) Transistor Demonstrated". The Silicon Engine: A Timeline of Semiconductors in Computers. Computer History Museum. Retrieved August 31, 2019.
^ Shirriff, Ken (30 August 2016). "The Surprising Story of the First Microprocessors". IEEE Spectrum. Institute of Electrical and Electronics Engineers. Retrieved 13 October 2019.
^ "1979: Single Chip Digital Signal Processor Introduced". The Silicon Engine. Computer History Museum. Retrieved 2019-05-13.
^ "DSPs: Back to the Future". ACM Queue. 2 (1). April 16, 2004. Retrieved 14 October 2019.
^ ^a ^b Billings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley. ISBN 978-1119943594.
^ ^a ^b Scharf, Louis L. (1991). Statistical signal processing: detection, estimation, and time series analysis. Boston: Addison–Wesley. ISBN 0-201-19038-9. OCLC 61160161.
^ Anastassiou, D. (2001). Genomic signal processing. IEEE.
^ 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.
^ Stoica, Petre; Moses, Randolph (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.
^ 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.

External links

Signal Processing for Communications – free online textbook by Paolo Prandoni and Martin Vetterli (2008)
Scientists and Engineers Guide to Digital Signal Processing – 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

[1] 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.

[2] Alan V. Oppenheim and Ronald W. Schafer (1989). Discrete-Time Signal Processing. Prentice Hall. p. 1. ISBN 0-13-216771-9.

[3] Oppenheim, Alan V.; Schafer, Ronald W. (1975). Digital Signal Processing. Prentice Hall. p. 5. ISBN 0-13-214635-5.

[4] "A Mathematical Theory of Communication - CHM Revolution". Computer History. Retrieved 2019-05-13.

[5] Fifty Years of Signal Processing. The IEEE Signal Processing Society. 1998.

[Grant-6] Grant, Duncan Andrew; Gowar, John (1989). Power MOSFETS: theory and applications. Wiley. p. 1. ISBN 9780471828679. 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.

[computerhistory-7] "1960: Metal Oxide Semiconductor (MOS) Transistor Demonstrated". The Silicon Engine: A Timeline of Semiconductors in Computers. Computer History Museum. Retrieved August 31, 2019.

[ieee-8] Shirriff, Ken (30 August 2016). "The Surprising Story of the First Microprocessors". IEEE Spectrum. Institute of Electrical and Electronics Engineers. Retrieved 13 October 2019.

[9] "1979: Single Chip Digital Signal Processor Introduced". The Silicon Engine. Computer History Museum. Retrieved 2019-05-13.

[10] "DSPs: Back to the Future". ACM Queue. 2 (1). April 16, 2004. Retrieved 14 October 2019.

[Billings-11] Billings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley. ISBN 978-1119943594.

[Scharf-12] Scharf, Louis L. (1991). Statistical signal processing: detection, estimation, and time series analysis. Boston: Addison–Wesley. ISBN 0-201-19038-9. OCLC 61160161.

[13] Anastassiou, D. (2001). Genomic signal processing. IEEE.

[Gaydecki2004-14] Patrick Gaydecki (2004). Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design. IET. pp. 40–. ISBN 978-0-85296-431-6.

[Engelberg2008-15] Shlomo Engelberg (8 January 2008). Digital Signal Processing: An Experimental Approach. Springer Science & Business Media. ISBN 978-1-84800-119-0.

[16] Boashash, Boualem, ed. (2003). Time frequency signal analysis and processing a comprehensive reference (1 ed.). Amsterdam: Elsevier. ISBN 0-08-044335-4.

[17] Stoica, Petre; Moses, Randolph (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.

[SchreierScharf2010-18] 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.

[Little2019-19] 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.

[DamelinJr2012-20] Steven B. Damelin; Willard Miller, Jr (2012). The Mathematics of Signal Processing. Cambridge University Press. ISBN 978-1-107-01322-3.

[PalomarEldar2010-21] Daniel P. Palomar; Yonina C. Eldar (2010). Convex Optimization in Signal Processing and Communications. Cambridge University Press. ISBN 978-0-521-76222-9.

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v t e Digital signal processing
Theory	Detection theory Discrete signal Estimation theory Nyquist–Shannon sampling theorem
Sub-fields	Audio signal processing Digital image processing Speech processing Statistical signal processing
Techniques	Z-transform Advanced z-transform Matched Z-transform method Bilinear transform Constant-Q transform Discrete cosine transform (DCT) Discrete Fourier transform (DFT) Discrete-time Fourier transform (DTFT) Impulse invariance Integral transform Laplace transform Post's inversion formula Starred transform Zak transform
Sampling	Aliasing Anti-aliasing filter Downsampling Nyquist rate / frequency Oversampling Quantization Sampling rate Undersampling Upsampling

Authority control databases
International	FAST
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Other	IdRef