Signal processing
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Signal processing is a subfield of mathematics, information and electrical engineering that concerns the analysis, synthesis, and modification of signals, which are broadly defined as functions conveying "information about the behavior or attributes of some phenomenon",^{[1]} such as sound, images, and biological measurements.^{[2]} For example, signal processing techniques are used to improve signal transmission fidelity, storage efficiency, and subjective quality, and to emphasize or detect components of interest in a measured signal.^{[3]}
Contents
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.^{[4]}
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 nonlinear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators and delay lines. Nonlinear circuits include compandors, multiplicators (frequency mixers and voltagecontrolled amplifiers), voltagecontrolled filters, voltagecontrolled oscillators and phaselocked loops.
Continuous time
Continuoustime 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 timeinvariant continuous system, integral of the system's zerostate response, setting up system function and the continuous time filtering of deterministic signals
Discrete time
Discretetime 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 discretetime signal processing is a technology based on electronic devices such as sample and hold circuits, analog timedivision 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 discretetime 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 discretetime sampled signals. Processing is done by generalpurpose computers or by digital circuits such as ASICs, fieldprogrammable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixedpoint and floatingpoint, realvalued and complexvalued, 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 spatiotemporal domains.^{[5]} 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.^{[6]} 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 420 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 ^{[7]}
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 analogtodigital 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 analogtodigital 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
 Recurrence relation
 Transform theory
 Timefrequency analysis – for processing nonstationary signals^{[8]}
 Spectral estimation – for determining the spectral content (i.e., the distribution of power over frequency) of a time series^{[9]}
 Statistical signal processing – analyzing and extracting information from signals and noise based on their stochastic properties
 Linear timeinvariant system theory, and transform theory
 System identification and classification
 Calculus
 Vector spaces and Linear algebra
 Functional analysis
 Probability and stochastic processes
 Detection theory
 Estimation theory
 Optimization
 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
See also
 Audio filter
 Dynamic range compression, companding, limiting, and noise gating
 Information theory
 Reverberation
Notes and references
 ^ Roland Priemer (1991). Introductory Signal Processing. World Scientific. p. 1. ISBN 9971509199.
 ^ Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstralbased statistical features". Computers in Biology and Medicine. 75 (1): 118–129. doi:10.1016/j.compbiomed.2016.05.013.
 ^ Alan V. Oppenheim and Ronald W. Schafer (1989). DiscreteTime Signal Processing. Prentice Hall. p. 1. ISBN 0132167719.
 ^ Oppenheim, Alan V.; Schafer, Ronald W. (1975). Digital Signal Processing. Prentice Hall. p. 5. ISBN 0132146355.
 ^ Billings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and SpatioTemporal Domains. Wiley. ISBN 1119943590.
 ^ Scharf, Louis L. (1991). Statistical signal processing: detection, estimation, and time series analysis. Boston: Addison–Wesley. ISBN 0201190389. OCLC 61160161.
 ^ Anastassiou, D. (2001). Genomic signal processing. IEEE.
 ^ Boashash, Boualem, ed. (2003). Time frequency signal analysis and processing a comprehensive reference (1 ed.). Amsterdam: Elsevier. ISBN 0080443354.
 ^ Stoica, Petre; Moses, Randolph (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.
Further reading
 P Stoica, R Moses (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.
 Kay, Steven M. (1993). Fundamentals of Statistical Signal Processing. Upper Saddle River, New Jersey: Prentice Hall. ISBN 0133457117. OCLC 26504848.
 Papoulis, Athanasios (1991). Probability, Random Variables, and Stochastic Processes (third ed.). McGrawHill. ISBN 0071008705.
 Kainam Thomas Wong [1]: Statistical Signal Processing lecture notes at the University of Waterloo, Canada.
 Ali H. Sayed, Adaptive Filters, Wiley, NJ, 2008, ISBN 9780470253885.
 Thomas Kailath, Ali H. Sayed, and Babak Hassibi, Linear Estimation, PrenticeHall, NJ, 2000, ISBN 9780130224644.
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
 BioMedical Signal processing at a Glance