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Digital signal processing (DSP) is the use of
digital processing Digital data, in information theory and information systems, is information represented as a string of discrete symbols each of which can take on one of only a finite number of values from some alphabet, such as letters or digit (unit), digits. An ...
, such as by computers or more specialized
digital signal processor The NeXTcube from 1990 had a Motorola 68040 (25 MHz) and a digital signal processor Motorola 56001">Motorola_68040.html" ;"title="NeXTcube from 1990 had a Motorola 68040">NeXTcube from 1990 had a Motorola 68040 (25 MHz) and a digital signal proce ...
s, to perform a wide variety of
signal processing 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 electromagnetis ...

signal processing
operations. The
digital signal A digital signal is a signal In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images ...
s processed in this manner are a sequence of numbers that represent
samples Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population - Complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of somet ...
of a
continuous variable In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...
in a domain such as time, space, or frequency. In
digital electronics Digital electronics is a field of electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electron is a subatomic particle In physica ...
, a digital signal is represented as a
pulse train In medicine Medicine is the Art (skill), art, science, and Praxis (process) , practice of caring for a patient and managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment or Palliative care , palliation of their ...
, which is typically generated by the switching of a
transistor upright=1.4, gate Candi bentar, a typical Indonesian gate that is often found on the islands of Java">Indonesia.html" ;"title="Candi bentar, a typical Indonesia">Candi bentar, a typical Indonesian gate that is often found on the islands o ...

transistor
. Digital signal processing and
analog signal processingAnalog signal processing is a type of signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and ...
are subfields of signal processing. DSP applications include
audio Audio most commonly refers to sound In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion ( ...
and
speech processing Speech processing is the study of speech Speech is human vocal communication using language. Each language uses Phonetics, phonetic combinations of vowel and consonant sounds that form the sound of its words (that is, all English words sound di ...
,
sonar Sonar (sound navigation and ranging) is a technique that uses 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, ...

sonar
,
radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

radar
and other
sensor array A sensor array is a group of sensors, usually deployed in a certain geometry pattern, used for collecting and processing electromagnetic or acoustic signals. The advantage of using a sensor array over using a single sensor lies in the fact that an a ...
processing,
spectral density estimation In statistical signal processing, the goal of spectral density estimation (SDE) is to estimate the spectral density (also known as the power spectral density) of a random signal from a sequence of time samples of the signal. Intuitively speaki ...
,
statistical signal processing 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 electromagnetis ...
,
digital image processing Digital image processing is the use of a digital computer A computer is a machine A machine is a man-made device that uses power to apply forces and control movement to perform an action. Machines can be driven by animals and people ...
,
data compression In signal processing 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, electro ...
,
video coding A video coding format (or sometimes video compression format) is a content representation format for storage or transmission of digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Har ...
,
audio coding An audio coding format (or sometimes audio compression format) is a Content format, content representation format for storage or transmission of digital audio (such as in digital television, digital radio and in audio and video files). Examples of ...
,
image compression Image compression is a type of data compression In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image proc ...
, signal processing for
telecommunication Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usually cylindrical A cylinder (from Greek Greek may refer to: Greece Anything of, from, or related to Greece Gr ...
s,
control system A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loop A control loop is the fundamental building block of industrial control systems. It consists of all the physical components a ...
s, biomedical engineering, and
seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "Earthquake, earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of Linear elasticity#Elastic wave, elast ...
, among others. DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to
nonlinear system identification System identification is a method of identifying or measuring the mathematical model A mathematical model is a description of a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rul ...
and can be implemented in the
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
,
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...
, and spatio-temporal domains. The application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as
error detection and correction In information theory Information theory is the scientific study of the quantification, storage, and communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an apparent answer to ...
in transmission as well as
data compression In signal processing 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, electro ...
. Digital signal processing is also fundamental to digital technology, such as digital telecommunication and
wireless communications Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points that do not use an electrical conductor In physics Physics (from grc, φυσική (ἐπιστήμη), ph ...
. DSP is applicable to both streaming data and static (stored) data.


Signal sampling

To digitally analyze and manipulate an analog signal, it must be digitized with an
analog-to-digital converter In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a Digital signal (signal processing), digit ...
(ADC). Sampling is usually carried out in two stages,
discretization A solution to a discretized partial differential equation, obtained with the finite element method. In applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics Physics (fro ...
and quantization. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set. Rounding
real numbers Real may refer to: * Reality, the state of things as they exist, rather than as they may appear or may be thought to be Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish col ...

real numbers
to integers is an example. The
Nyquist–Shannon sampling theorem The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing Signal processing is an electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of ...
states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is often significantly higher than this. Theoretical DSP analyses and derivations are typically performed on
discrete-time signalIn mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time. Discrete time Discrete sampled signal Discrete time views values of variables as occurring at disti ...
models with no amplitude inaccuracies (
quantization error Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite Cardinality, number of elements. Ro ...

quantization error
), "created" by the abstract process of
sampling Sampling may refer to: *Sampling (signal processing), converting a continuous signal into a discrete signal *Sample (graphics), Sampling (graphics), converting continuous colors into discrete color components *Sampling (music), the reuse of a sound ...
. Numerical methods require a quantized signal, such as those produced by an ADC. The processed result might be a frequency spectrum or a set of statistics. But often it is another quantized signal that is converted back to analog form by a
digital-to-analog converter In , a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a into an . An (ADC) performs the reverse function. There are several DAC ; the suitability of a DAC for a particular application is determined by ...
(DAC).


Domains

In DSP, engineers usually study digital signals in one of the following domains:
time domain Time domain refers to the analysis of mathematical functions Mathematics (from Greek: ) includes the study of such topics as quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity ...
(one-dimensional signals), spatial domain (multidimensional signals),
frequency domain In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or Signal (information theory), signals with respect to frequency, rather than time. Put simply, a time-dom ...
, and
wavelet A wavelet is a wave In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion a ...

wavelet
domains. They choose the domain in which to process a signal by making an informed assumption (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a
discrete Fourier transform In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discret ...
produces the frequency domain representation.


Time and space domains

Time domain Time domain refers to the analysis of mathematical functions Mathematics (from Greek: ) includes the study of such topics as quantity Quantity is a property that can exist as a multitude or magnitude, which illustrate discontinuity ...
refers to the analysis of signals with respect to time. Similarly, space domain refers to the analysis of signals with respect to position, e.g., pixel location for the case of image processing. The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering.
Digital filter In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scientific measurements. Signal ...
ing generally consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. The surrounding samples may be identified with respect to time or space. The output of a linear digital filter to any given input may be calculated by convolving the input signal with an
impulse response In , the impulse response, or impulse response function (IRF), of a is its output when presented with a brief input signal, called an . More generally, an impulse response is the reaction of any dynamic system in response to some external change. ...

impulse response
.


Frequency domain

Signals are converted from time or space domain to the frequency domain usually through use of the
Fourier transform#REDIRECT Fourier transform In mathematics, a Fourier transform (FT) is a Integral transform, mathematical transform that decomposes function (mathematics), functions depending on space or time into functions depending on spatial or temporal frequenc ...
. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant, often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. Frequency domain analysis is also called ''spectrum-'' or ''spectral analysis''. Filtering, particularly in non-realtime work can also be achieved in the frequency domain, applying the filter and then converting back to the time domain. This can be an efficient implementation and can give essentially any filter response including excellent approximations to brickwall filters. There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the harmonic structure of the original spectrum.


Z-plane analysis

Digital filters come in both IIR and FIR types. Whereas FIR filters are always stable, IIR filters have feedback loops that may become unstable and oscillate. The
Z-transform In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...
provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the
Laplace transform In mathematics, the Laplace transform, named after its inventor Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable t (often time in physics, time) to a function of a complex analysis, complex variable s (co ...
, which is used to design and analyze analog IIR filters.


Autoregression analysis

A signal is represented as linear combination of its previous samples. Coefficients of the combination are called autoregression coefficients. This method has higher frequency resolution and can process shorter signals compared to the Fourier transform.
Prony's method Prony analysis (Prony's method) was developed by Gaspard Riche de Prony in 1795. However, practical use of the method awaited the digital computer. Similar to the Fourier transform, Prony's method extracts valuable information from a uniformly sampl ...
can be used to estimate phases, amplitudes, initial phases and decays of the components of signal. Components are assumed to be complex decaying exponents.


Time-frequency analysis

A time-frequency representation of signal can capture both temporal evolution and frequency structure of analyzed signal. Temporal and frequency resolution are limited by the principle of uncertainty and the tradeoff is adjusted by the width of analysis window. Linear techniques such as
Short-time Fourier transform The Short-time Fourier transform (STFT), is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divid ...
,
wavelet transform In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
,
filter bankIn signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency Sub-band coding, sub-band of the original signal. One application of a ...
, non-linear (e.g., Wigner — Ville transform) and
autoregressive In statistics Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with ...
methods (e.g. segmented Prony method) are used for representation of signal on the time-frequency plane. Non-linear and segmented Prony methods can provide higher resolution, but may produce undesireable artefacts. Time-frequency analysis is usually used for analysis of non-stationary signals. For example, methods of
fundamental frequency The fundamental frequency, often referred to simply as the fundamental, is defined as the lowest frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is t ...
estimation, such as RAPT and PEFAC are based on windowed spectral analysis.


Wavelet

In
numerical analysis Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic computation, symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis ...
and
functional analysis 200px, One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis. Functional analysis is a branch of mathemat ...
, a
discrete wavelet transform . The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is hig ...
is any
wavelet transform In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
for which the
wavelet A wavelet is a wave In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion a ...

wavelet
s are discretely sampled. As with other wavelet transforms, a key advantage it has over
Fourier transform#REDIRECT Fourier transform In mathematics, a Fourier transform (FT) is a Integral transform, mathematical transform that decomposes function (mathematics), functions depending on space or time into functions depending on spatial or temporal frequenc ...
s is temporal resolution: it captures both frequency ''and'' location information. The accuracy of the joint time-frequency resolution is limited by the
uncertainty principle In quantum mechanics Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quant ...

uncertainty principle
of time-frequency.


Empirical mode decomposition

Empirical mode decomposition is based on decomposition signal into intrinsic mode functions (IMF). IMFs are quasiharmonical oscillations that are extracted from the signal.


Implementation

DSP
algorithm In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always and are used as specifications for performing s, , , and other ...

algorithm
s may be run on general-purpose computers and
digital signal processor The NeXTcube from 1990 had a Motorola 68040 (25 MHz) and a digital signal processor Motorola 56001">Motorola_68040.html" ;"title="NeXTcube from 1990 had a Motorola 68040">NeXTcube from 1990 had a Motorola 68040 (25 MHz) and a digital signal proce ...
s. DSP algorithms are also implemented on purpose-built hardware such as
application-specific integrated circuit An application-specific integrated circuit (ASIC ) is an integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit File:PExdcr01CJC.jpg, ...
(ASICs). Additional technologies for digital signal processing include more powerful general purpose
microprocessor A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip ...

microprocessor
s,
graphics processing unit A graphics processing unit (GPU) is a specialized electronic circuit 200px, A circuit built on a printed circuit board (PCB). An electronic circuit is composed of individual electronic component An electronic component is any basic discre ...
s,
field-programmable gate array A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturinghence the term ''Field-programmability, field-programmable''. The FPGA configuration is generally specifie ...
s (FPGAs), digital signal controllers (mostly for industrial applications such as motor control), and stream processors. For systems that do not have a
real-time computing Real-time computing (RTC) is the computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Comput ...
requirement and the signal data (either input or output) exists in data files, processing may be done economically with a general-purpose computer. This is essentially no different from any other
data processing Data processing is, generally, "the collection Collection or Collections may refer to: * Cash collection, the function of an accounts receivable department * Collection agency, agency to collect cash * Collections management (museum) ** Colle ...

data processing
, except DSP mathematical techniques (such as the DCT and
FFT A fast Fourier transform (FFT) is an algorithm of an algorithm (Euclid's algorithm) for calculating the greatest common divisor (g.c.d.) of two numbers ''a'' and ''b'' in locations named A and B. The algorithm proceeds by successive subtract ...
) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. An example of such an application is processing digital photographs with software such as
Photoshop Adobe Photoshop is a raster graphics editor A screenshot from the GIMP raster graphics editor. A raster graphics editor is a computer program A computer program is a collection of instructions that can be executed by a computer to perfo ...
. When the application requirement is real-time, DSP is often implemented using specialized or dedicated processors or microprocessors, sometimes using multiple processors or multiple processing cores. These may process data using fixed-point arithmetic or floating point. For more demanding applications
FPGA A field-programmable gate array (FPGA) is an integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit 200px, A circuit built on a pr ...
s may be used. For the most demanding applications or high-volume products,
ASIC An application-specific integrated circuit (ASIC ) is an integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuit 200px, A circuit b ...
s might be designed specifically for the application. is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional 3rd party DSP chips located on extension cards or external hardware boxes or racks. Many
digital audio workstation A digital audio workstation (DAW) is an electronic device or application software Application software (app for short) is computing software designed to carry out a specific task other than one relating to the operation of the computer itsel ...
s such as
Logic Pro Logic Pro is a digital audio workstation A digital audio workstation (DAW) is an electronic device or application software Application software (app for short) is computing software designed to carry out a specific task other than one ...
,
Cubase Cubase is a digital audio workstation A digital audio workstation (DAW) is an electronic device or application software Application software (app for short) is computing software designed to carry out a specific task other than one relat ...
,
Digital Performer Digital Performer is a Digital Audio Workstation set-up A digital audio workstation (DAW) is an electronic device or application software used for recording, editing and producing audio files. DAWs come in a wide variety of configurations ...
and
Pro Tools Pro Tools is a digital audio workstation (DAW) developed and released by Avid Technology (formerly Avid Audio, Digidesign) for Microsoft Windows and OS X, macOS. It is used for music creation and production, sound for picture (sound design, aud ...
LE use native processing. Others, such as
Pro Tools Pro Tools is a digital audio workstation (DAW) developed and released by Avid Technology (formerly Avid Audio, Digidesign) for Microsoft Windows and OS X, macOS. It is used for music creation and production, sound for picture (sound design, aud ...
HD, Universal Audio's UAD-1 and
TC Electronic TC Electronic is a Denmark, Danish audio equipment company that designs and imports Effects unit, guitar effects, bass amplification, computer audio interfaces, audio plug-in software, live sound Equalization (audio), equalisers, studio and post p ...
's Powercore use DSP processing.


Applications

General application areas for DSP include *
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, consisting ...
*
Audio data compression In signal processing 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, electro ...
e.g.
MP3 MP3 (formally MPEG-1 Audio Layer III or MPEG-2 Audio Layer III) is a coding format for digital audio Digital audio is a representation of sound recorded in, or converted into, Digital signal (signal processing), digital form. In digital a ...

MP3
* Video data compression *
Computer graphics Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great dea ...

Computer graphics
*
Digital image processing Digital image processing is the use of a digital computer A computer is a machine A machine is a man-made device that uses power to apply forces and control movement to perform an action. Machines can be driven by animals and people ...
*
Photo manipulation Photograph manipulation involves the transformation or alteration of a photograph A photograph (also known as a photo) is an image An SAR radar image acquired by the SIR-C/X-SAR radar on board the Space Shuttle Endeavour show ...
*
Speech processing Speech processing is the study of speech Speech is human vocal communication Communication (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was ...
*
Speech recognition Speech recognition is an interdisciplinary Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic discipline An academic discipline or academic field is a subdivision of knowledge that is Educa ...

Speech recognition
*
Data transmission Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data Data (; ) are individual facts, statistics, or items of information, often numeric. In a more techn ...

Data transmission
*
Radar Radar (radio detection and ranging) is a detection system that uses radio waves to determine the distance (''ranging''), angle, or velocity of objects. It can be used to detect aircraft, Marine radar, ships, spacecraft, guided missiles, motor ...

Radar
*
Sonar Sonar (sound navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigation, navigate, measure distances (ranging), communicate with or detect objects on or under the surface o ...

Sonar
*
Financial signal processing Financial signal processing is a branch of signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, image ...
*
Economic forecasting Economic forecasting is the process of making predictions about the economy. Forecasts can be carried out at a high level of aggregation—for example for GDP, inflation In economics Economics () is the social science that studies h ...
*
Seismology Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "Earthquake, earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes and the propagation of Linear elasticity#Elastic wave, elast ...
*
Biomedicine Biomedicine (also referred to as Western medicine, mainstream medicine or conventional medicine)
*
Weather forecasting Weather forecasting is the application of science and technology to predict the conditions of the atmosphere An atmosphere (from the greek words ἀτμός ''(atmos)'', meaning 'vapour', and σφαῖρα ''(sphaira)'', meaning 'ball' o ...
Specific examples include
speech coding Speech coding is an application of data compression In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image ...
and transmission in digital
mobile phone A mobile phone, cellular phone, cell phone, cellphone, handphone, or hand phone, sometimes shortened to simply mobile, cell or just phone, is a portable telephone A telephone is a telecommunication Telecommunication is the tra ...

mobile phone
s, room correction of sound in hi-fi and sound reinforcement applications, analysis and control of industrial processes, medical imaging such as Computed axial tomography, CAT scans and MRI, audio crossovers and equalization (audio), equalization, digital synthesizers, and audio effects units.


Techniques

* Bilinear transform * Discrete Fourier transform * Discrete-time Fourier transform * Filter design * Goertzel algorithm * LTI system theory * Minimum phase * s-plane * Transfer function *
Z-transform In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It h ...


Related fields

* Analog signal processing * Automatic control * Computer engineering * Computer science * Data compression * Dataflow programming * Discrete cosine transform * Electrical engineering * Fourier analysis * Information theory * Machine learning * Real-time computing * Stream processing * Telecommunication * Time series * Wavelet


Further reading

* *Jonathan M. Blackledge, Martin Turner: ''Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications'', Horwood Publishing, *James D. Broesch: ''Digital Signal Processing Demystified'', Newnes, * *Paul M. Embree, Damon Danieli: ''C++ Algorithms for Digital Signal Processing'', Prentice Hall, *Hari Krishna Garg: ''Digital Signal Processing Algorithms'', CRC Press, *P. Gaydecki: ''Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design'', Institution of Electrical Engineers, *Ashfaq Khan: ''Digital Signal Processing Fundamentals'', Charles River Media, *Sen M. Kuo, Woon-Seng Gan: ''Digital Signal Processors: Architectures, Implementations, and Applications'', Prentice Hall, *Paul A. Lynn, Wolfgang Fuerst: ''Introductory Digital Signal Processing with Computer Applications'', John Wiley & Sons, *Richard G. Lyons: ''Understanding Digital Signal Processing'', Prentice Hall, *Vijay Madisetti, Douglas B. Williams: ''The Digital Signal Processing Handbook'', CRC Press, *James H. McClellan, Ronald W. Schafer, Mark A. Yoder: ''Signal Processing First'', Prentice Hall, *Bernard Mulgrew, Peter Grant, John Thompson: ''Digital Signal Processing – Concepts and Applications'', Palgrave Macmillan, *Boaz Porat: ''A Course in Digital Signal Processing'', Wiley, *John G. Proakis, Dimitris Manolakis: ''Digital Signal Processing: Principles, Algorithms and Applications'', 4th ed, Pearson, April 2006, *John G. Proakis: ''A Self-Study Guide for Digital Signal Processing'', Prentice Hall, *Charles A. Schuler: ''Digital Signal Processing: A Hands-On Approach'', McGraw-Hill, *Doug Smith: ''Digital Signal Processing Technology: Essentials of the Communications Revolution'', American Radio Relay League, * * * * * *Hayes, Monson H. Statistical digital signal processing and modeling. John Wiley & Sons, 2009. (wit
MATLAB scripts


References

{{DEFAULTSORT:Digital Signal Processing Digital signal processing, Digital electronics Computer engineering Telecommunication theory Computer science Radar signal processing