Signal processing

Encyclopedia

**Signal processing**is an area of systems engineering

Systems engineering

Systems engineering is an interdisciplinary field of engineering that focuses on how complex engineering projects should be designed and managed over the life cycle of the project. Issues such as logistics, the coordination of different teams, and automatic control of machinery become more...

, electrical engineering

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

and applied mathematics

Applied mathematics

Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...

that deals with operations on or analysis of signals, in either discrete or continuous time. Signals of interest can include sound

Audio signal processing

Audio signal processing, sometimes referred to as audio processing, is the intentional alteration of auditory signals, or sound. As audio signals may be electronically represented in either digital or analog format, signal processing may occur in either domain...

, images

Image processing

In electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...

, time-varying measurement values and sensor

Sensor

A sensor is a device that measures a physical quantity and converts it into a signal which can be read by an observer or by an instrument. For example, a mercury-in-glass thermometer converts the measured temperature into expansion and contraction of a liquid which can be read on a calibrated...

data, for example biological data such as electrocardiogram

Electrocardiogram

Electrocardiography is a transthoracic interpretation of the electrical activity of the heart over a period of time, as detected by electrodes attached to the outer surface of the skin and recorded by a device external to the body...

s, control system

Control system

A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...

signals, telecommunication transmission

Transmission (telecommunications)

Transmission, in telecommunications, is the process of sending, propagating and receiving an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless...

signals, and many others. Signals are analog or digital electrical representations of time-varying or spatial-varying physical quantities. In the context of signal processing, arbitrary binary data streams and on-off signalling

Signalling (telecommunications)

In telecommunication, signaling has the following meanings:*the use of signals for controlling communications...

are not considered as signals, but only analog and digital signals that are representations of analog physical quantities.

## Typical operations and applications

Processing of signals includes the following operations and algorithms with application examples:- FilteringElectronic filterElectronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...

(for example in tone controls and equalizers) - SmoothingSmoothingIn statistics and image processing, to smooth a data set is to create an approximating function that attempts to capture important patterns in the data, while leaving out noise or other fine-scale structures/rapid phenomena. Many different algorithms are used in smoothing...

, deblurring (for example in image enhancement) - Adaptive filterAdaptive filterAn adaptive filter is a filter that self-adjusts its transfer function according to an optimization algorithm driven by an error signal. Because of the complexity of the optimization algorithms, most adaptive filters are digital filters. By way of contrast, a non-adaptive filter has a static...

ing (for example for echo-cancellation in a conference telephone, or denoising for aircraft identification by radar) - Spectrum analysisSpectrum analyzerA spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals...

(for example in magnetic resonance imagingMagnetic resonance imagingMagnetic resonance imaging , nuclear magnetic resonance imaging , or magnetic resonance tomography is a medical imaging technique used in radiology to visualize detailed internal structures...

, tomographic reconstructionTomographic reconstructionThe mathematical basis for tomographic imaging was laid down by Johann Radon. It is applied in computed tomography to obtain cross-sectional images of patients...

and OFDM modulation) - Digitization, reconstruction and compressionData compressionIn computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....

(for example, image compressionImage compressionThe objective of image compression is to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form.- Lossy and lossless compression :...

, sound coding and other source codingSource codingIn information theory, Shannon's source coding theorem establishes the limits to possible data compression, and the operational meaning of the Shannon entropy....

) - Storage (in digital delay lineDigital delay lineA digital delay line is a discrete element in digital filter theory, which allows a signal to be delayed by a number of samples. If the delay is an integer multiple of samples digital delay lines are often implemented as circular buffers...

s and reverb) - ModulationModulationIn electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...

(in modemModemA modem is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data...

s and radio receivers and transmitters) - Wavetable synthesisWavetable synthesisWavetable synthesis is used in certain digital music synthesizers to implement a restricted form of real-time additive synthesis. The technique was first developed by Wolfgang Palm of PPG in the late 1970s and published in 1979, and has since been used as the primary synthesis method in...

(in modemModemA modem is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data...

s and music synthesizerSynthesizerA synthesizer is an electronic instrument capable of producing sounds by generating electrical signals of different frequencies. These electrical signals are played through a loudspeaker or set of headphones...

s) - Feature extractionFeature extractionIn pattern recognition and in image processing, feature extraction is a special form of dimensionality reduction.When the input data to an algorithm is too large to be processed and it is suspected to be notoriously redundant then the input data will be transformed into a reduced representation...

(for example speech-to-textSpeech recognitionSpeech recognition converts spoken words to text. The term "voice recognition" is sometimes used to refer to recognition systems that must be trained to a particular speaker—as is the case for most desktop recognition software...

conversion and optical character recognitionOptical character recognitionOptical character recognition, usually abbreviated to OCR, is the mechanical or electronic translation of scanned images of handwritten, typewritten or printed text into machine-encoded text. It is widely used to convert books and documents into electronic files, to computerize a record-keeping...

) - Pattern recognitionPattern recognitionIn machine learning, pattern recognition is the assignment of some sort of output value to a given input value , according to some specific algorithm. An example of pattern recognition is classification, which attempts to assign each input value to one of a given set of classes...

and correlationCorrelationIn statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

analysis (in spread spectrumSpread spectrumSpread-spectrum techniques are methods by which a signal generated in a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth...

receivers and computer visionComputer visionComputer vision is a field that includes methods for acquiring, processing, analysing, and understanding images and, in general, high-dimensional data from the real world in order to produce numerical or symbolic information, e.g., in the forms of decisions...

) - PredictionPredictionA prediction or forecast is a statement about the way things will happen in the future, often but not always based on experience or knowledge...

- A variety of other operations

In communication systems, signal processing may occur at OSI layer

OSI model

The Open Systems Interconnection model is a product of the Open Systems Interconnection effort at the International Organization for Standardization. It is a prescription of characterizing and standardizing the functions of a communications system in terms of abstraction layers. Similar...

1, the Physical Layer

Physical layer

The physical layer or layer 1 is the first and lowest layer in the seven-layer OSI model of computer networking. The implementation of this layer is often termed PHY....

(modulation

Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...

, equalization

Equalization

Equalization, is the process of adjusting the balance between frequency components within an electronic signal. The most well known use of equalization is in sound recording and reproduction but there are many other applications in electronics and telecommunications. The circuit or equipment used...

, multiplexing

Multiplexing

The multiplexed signal is transmitted over a communication channel, which may be a physical transmission medium. The multiplexing divides the capacity of the low-level communication channel into several higher-level logical channels, one for each message signal or data stream to be transferred...

, etc.) in the seven layer OSI model, as well as at OSI layer 6, the Presentation Layer

Presentation layer

The presentation layer is layer 6 of the seven-layer OSI model of computer networking and serves as the data translator for the network. It is sometimes called the syntax layer.-Description:...

(source coding, including analog-to-digital conversion

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

and data compression

Data compression

In computer science and information theory, data compression, source coding or bit-rate reduction is the process of encoding information using fewer bits than the original representation would use....

).

## History

According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysisNumerical analysis

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....

techniques of the 17th century. They further state that the "digitalization" or digital refinement of these techniques can be found in the digital control system

Control system

A control system is a device, or set of devices to manage, command, direct or regulate the behavior of other devices or system.There are two common classes of control systems, with many variations and combinations: logic or sequential controls, and feedback or linear controls...

s of the 1940s and 1950s.

## Mathematical topics embraced by signal processing

- Linear signals and systems, and transform theoryTransform theoryIn mathematics, transform theory is the study of transforms. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory.-Spectral theory:...
- System identificationSystem identificationIn control engineering, the field of system identification uses statistical methods to build mathematical models of dynamical systems from measured data...

and classification - CalculusCalculusCalculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
- Differential equations
- Vector spaces and Linear algebraLinear algebraLinear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
- Functional analysisFunctional analysisFunctional 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 and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
- ProbabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

and stochastic processes - Detection theoryDetection theoryDetection theory, or signal detection theory, is a means to quantify the ability to discern between information-bearing energy patterns and random energy patterns that distract from the information Detection theory, or signal detection theory, is a means to quantify the ability to discern between...
- Estimation theoryEstimation theoryEstimation theory is a branch of statistics and signal processing 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 value affects the distribution of the...
- Optimization
- Programming
- Numerical methods
- Iterative methods

### Analog signal processing

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 such as passive filters, active filterActive filter

An active filter is a type of analog electronic filter that uses an amplifier stage. Amplifiers included in a filter design can be used to improve the performance, stability and predictability of a filter. An amplifier prevents the impedance of source or load stages from affecting the...

s, additive mixers

Electronic mixer

An electronic mixer is a device that combines two or more electrical or electronic signals into one or two composite output signals. There are two basic circuits that both use the term mixer, but they are very different types of circuits: additive mixers and multiplying mixers...

, integrator

Integrator

An integrator is a device to perform the mathematical operation known as integration, a fundamental operation in calculus.The integration function is often part of engineering, physics, mechanical, chemical and scientific calculations....

s and delay line

Delay line

Delay line may refer to:* Propagation delay, the length of time taken for something to reach its destination* Analog delay line, used to delay a signal...

s. It also involves non-linear circuits such as compandors, multiplicators (frequency mixer

Frequency mixer

In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...

s and voltage-controlled amplifiers), voltage-controlled filter

Voltage-controlled filter

A voltage-controlled filter is a filter whose operating characteristics can be controlled by means of a control voltage applied to one or more inputs...

s, voltage-controlled oscillator

Voltage-controlled oscillator

A voltage-controlled oscillator or VCO is an electronic oscillator designed to be controlled in oscillation frequency by a voltage input. The frequency of oscillation is varied by the applied DC voltage, while modulating signals may also be fed into the VCO to cause frequency modulation or phase...

s and phase-locked loop

Phase-locked loop

A phase-locked loop or phase lock loop is a control system that generates an output signal whose phase is related to the phase of an input "reference" signal. It is an electronic circuit consisting of a variable frequency oscillator and a phase detector...

s.

### Discrete time signal processing

Discrete time signal processing is for sampled signals that are considered as 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

Sample and hold

In electronics, a sample and hold circuit is an analog device that samples the voltage of a continuously varying analog signal and holds its value at a constant level for a specified minimal period of time. Sample and hold circuits and related peak detectors are the elementary analog memory...

circuits, analog time-division multiplexer

Multiplexer

In electronics, a multiplexer is a device that selects one of several analog or digital input signals and forwards the selected input into a single line. A multiplexer of 2n inputs has n select lines, which are used to select which input line to send to the output...

s, analog delay line

Analog delay line

An analog delay line is a network of electrical components connected in series; where each individual element creates a time difference or phase change between its input signal and its output signal. An example is a bucket-brigade device....

s 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

Quantization error

In analog-to-digital conversion, the difference between the actual analog value and quantized digital value is called quantization error or quantization distortion. This error is either due to rounding or truncation...

into consideration.

### Digital signal processing

Digital signal processing is the processing of digitised discrete time sampled signals. Processing is done by general-purpose computerComputer

A computer is a programmable machine designed to sequentially and automatically carry out a sequence of arithmetic or logical operations. The particular sequence of operations can be changed readily, allowing the computer to solve more than one kind of problem...

s or by digital circuits such as ASIC

Application-specific integrated circuit

An application-specific integrated circuit is an integrated circuit customized for a particular use, rather than intended for general-purpose use. For example, a chip designed solely to run a cell phone is an ASIC...

s, field-programmable gate array

Field-programmable gate array

A field-programmable gate array is an integrated circuit designed to be configured by the customer or designer after manufacturing—hence "field-programmable"...

s or specialized digital signal processor

Digital signal processor

A digital signal processor is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.-Typical characteristics:...

s (DSP chips). Typical arithmetical operations include fixed-point

Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after the radix point...

and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffer

Circular buffer

A circular buffer, cyclic buffer or ring buffer is a data structure that uses a single, fixed-size buffer as if it were connected end-to-end.This structure lends itself easily to buffering data streams.-Uses:...

s and look-up tables. Examples of algorithms are the Fast Fourier transform

Fast Fourier transform

A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...

(FFT), finite impulse response

Finite impulse response

A finite impulse response filter is a type of a signal processing filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response filters, which have internal feedback and may continue to respond indefinitely...

(FIR) filter, Infinite impulse response

Infinite impulse response

Infinite impulse response is a property of signal processing systems. Systems with this property are known as IIR systems or, when dealing with filter systems, as IIR filters. IIR systems have an impulse response function that is non-zero over an infinite length of time...

(IIR) filter, and adaptive filter

Adaptive filter

An adaptive filter is a filter that self-adjusts its transfer function according to an optimization algorithm driven by an error signal. Because of the complexity of the optimization algorithms, most adaptive filters are digital filters. By way of contrast, a non-adaptive filter has a static...

s such as the Wiener

Wiener filter

In signal processing, the Wiener filter is a filter proposed by Norbert Wiener during the 1940s and published in 1949. Its purpose is to reduce the amount of noise present in a signal by comparison with an estimation of the desired noiseless signal. The discrete-time equivalent of Wiener's work was...

and Kalman filter

Kalman filter

In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...

s.

## Fields of signal processing

- Statistical signal processingStatistical signal processingStatistical signal processing is an area of Applied Mathematics and Signal Processing that treats signals as stochastic processes, dealing with their statistical properties...

— analyzing and extracting information from signals and noise based on their stochastic properties - Audio signal processingAudio signal processingAudio signal processing, sometimes referred to as audio processing, is the intentional alteration of auditory signals, or sound. As audio signals may be electronically represented in either digital or analog format, signal processing may occur in either domain...

— for electrical signals representing sound, such as speech or music - Speech signal processingSpeech signal processingSpeech signal processing refers to the acquisition, manipulation, storage, transfer and output of vocal utterances by a computer. The main applications are the recognition, synthesis and compression of human speech:...

— for processing and interpreting spoken words - Image processingImage processingIn electrical engineering and computer science, image processing is any form of signal processing for which the input is an image, such as a photograph or video frame; the output of image processing may be either an image or, a set of characteristics or parameters related to the image...

— in digital cameras, computers, and various imaging systems - Video processingVideo processingIn electrical engineering and computer science, video processing is a particular case of signal processing, which often employs video filters and where the input and output signals are video files or video streams. Video processing techniques are used in television sets, VCRs, DVDs, video codecs,...

— for interpreting moving pictures - Array processingArray processingArray processing is signal processing of the outputs of an array of sensors to:* Enhance the signal-to-interference-plus-noise ratio compared to that of a single sensor using conventional or adaptive beamforming....

— for processing signals from arrays of sensors - Time-frequency signal processingTime-frequency analysisIn signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations...

— for processing non-stationary signals - FilteringFilter (signal processing)In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

— used in many fields to process signals - Seismic signal processing
- Data miningData miningData mining , a relatively young and interdisciplinary field of computer science is the process of discovering new patterns from large data sets involving methods at the intersection of artificial intelligence, machine learning, statistics and database systems...

.

## 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 and Recognition Group