Signal processing is an

electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

subfield that focuses on analyzing, modifying and synthesizing '' signals'', such as

sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...

, images, and

scientific measurements In mathematics and empirical science, quantification (or quantitation) is the act of counting and measuring that maps human sense observations and experiences into quantity, quantities. Quantification in this sense is fundamental to the scientific ...

. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal.

History

According to

Alan V. Oppenheim Alan Victor Oppenheim''Alan Victor Oppenheim'' was elected in 1987

and Ronald W. Schafer, the principles of signal processing can be found in the classical

numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods th ...

techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital

control system A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial ...

s of the 1940s and 1950s. In 1948,

Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts In ...

wrote the influential paper " A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission. Signal processing matured and flourished in the 1960s and 1970s, and digital signal processing became widely used with specialized digital signal processor chips in the 1980s.

Categories

Analog

Analog signal processing is for signals that have not been digitized, as in most 20th-century

radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transm ...

, telephone, 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, multipliers ( frequency mixers, 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 Time domain refers to the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the ...

frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a ...

, 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 In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

, 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 A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis converts a signal from its original domain (often time or space) to a representation in t ...

(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. Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and

subharmonics In music, the undertone series or subharmonic series is a sequence of notes that results from inverting the intervals of the overtone series. While overtones naturally occur with the physical production of music on instruments, undertones must ...

which cannot be produced or analyzed using linear methods. Polynomial signal processing is a type of non-linear signal processing, where

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An ex ...

systems may be interpreted as conceptually straight forward extensions of linear systems to the non-linear case.

Statistical

Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. Statistical techniques are widely used in signal processing applications. For example, one can model the

probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomeno ...

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 Audio signal processing is a subfield of signal processing that is concerned with the electronic manipulation of audio signals. Audio signals are electronic representations of sound waves— longitudinal waves which travel through air, consist ...

for electrical signals representing sound, such as

speech Speech is a human vocal communication using language. Each language uses phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound different from all French words, even if they are th ...

or music * Image processing in digital cameras, computers and various imaging systems * Video processing for interpreting moving pictures *

Wireless communication Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The mos ...

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 Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of elastic waves through the Earth or through other ...

* Financial signal processing analyzing financial data using signal processing techniques, especially for prediction purposes. * Feature extraction, such as image understanding and

speech recognition Speech recognition is an interdisciplinary subfield of computer science and computational linguistics that develops methodologies and technologies that enable the recognition and translation of spoken language into text by computers with the ma ...

. * Quality improvement, such as noise reduction, image enhancement, and

echo cancellation Echo suppression and echo cancellation are methods used in telephony to improve voice quality by preventing echo from being created or removing it after it is already present. In addition to improving subjective audio quality, echo suppression ...

. * Source coding including audio compression, image compression, and video compression. * Genomic signal processing In communication systems, signal processing may occur at: *

OSI layer The Open Systems Interconnection model (OSI model) is a conceptual model that 'provides a common basis for the coordination of SOstandards development for the purpose of systems interconnection'. In the OSI reference model, the communications ...

1 in the seven layer OSI model, the physical layer (

modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the '' carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informat ...

, equalization,

multiplexing In telecommunications and computer networking, multiplexing (sometimes contracted to muxing) is a method by which multiple analog or digital signals are combined into one signal over a shared medium. The aim is to share a scarce resource - a ...

, 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

data compression In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compressi ...

Typical devices

Filters Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component th ...

for example analog (passive or active) or digital (

FIR Firs (''Abies'') are a genus of 48–56 species of evergreen coniferous trees in the family (biology), family Pinaceae. They are found on mountains throughout much of North America, North and Central America, Europe, Asia, and North Africa. The ...

, 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 In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...

* Recurrence relations * Transform theory * Time-frequency analysis for processing non-stationary signals *

Spectral estimation In statistical signal processing, the goal of spectral density estimation (SDE) or simply spectral estimation is to estimate the spectral density (also known as the power spectral density) of a signal from a sequence of time samples of the s ...

for determining the spectral content (i.e., the distribution of power over frequency) of a time series * 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 The field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data f ...

and classification *

Calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...

Complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebra ...

* Vector spaces and

Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matric ...

Functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined ...

Probability Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and ...

and stochastic processes *

Detection theory Detection theory or signal detection theory is a means to measure the ability to differentiate between information-bearing patterns (called stimulus in living organisms, signal in machines) and random patterns that distract from the information ( ...

Estimation theory Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their val ...

* Optimization * Numerical methods *

Time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. E ...

* 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

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 {{Authority control Mass media technology Telecommunication theory