Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized

digital signal processor A digital signal processor (DSP) is a specialized microprocessor chip, with its architecture optimized for the operational needs of digital signal processing. DSPs are fabricated on MOS integrated circuit chips. They are widely used in audio si ...

s, to perform a wide variety of signal processing operations. The

digital signal A digital signal is a signal that represents data as a sequence of discrete values; at any given time it can only take on, at most, one of a finite number of values. This contrasts with an analog signal, which represents continuous values; at ...

s processed in this manner are a sequence of numbers that represent samples of a

continuous variable In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by ''measuring'' or ''counting'', respectively. If it can take on two particular real values such that it can also take on all re ...

in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing,

spectral density 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 signa ...

, statistical signal processing, digital image processing, data compression, video coding, audio coding,

image compression Image compression is a type of data compression applied to digital images, to reduce their cost for storage or transmission. Algorithms may take advantage of visual perception and the statistical properties of image data to provide superior r ...

, signal processing for telecommunications,

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 c ...

s, biomedical engineering, and seismology, among others. DSP can involve linear or nonlinear operations. Nonlinear signal processing is closely related to nonlinear system identification and can be implemented in the time, frequency, 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 and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communi ...

in transmission as well as data compression. Digital signal processing is also fundamental to digital technology, such as digital telecommunication and wireless communications. 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 (ADC). Sampling is usually carried out in two stages,

discretization In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...

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 In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real ...

to integers is an example. The Nyquist–Shannon sampling theorem 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 signal In mathematical dynamics, discrete time and continuous time are two alternative frameworks within which variables that evolve over time are modeled. Discrete time Discrete time views values of variables as occurring at distinct, separate "po ...

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 number of elements. Rounding and ...

), "created" by the abstract process of sampling. 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 (DAC).

Domains

DSP engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and 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 produces the frequency domain representation.

Time and space domains

Time domain 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 filtering 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 signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an Dirac delta function, impulse (). More generally, an impulse ...

Frequency domain

Signals are converted from time or space domain to the frequency domain usually through use of the

Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...

. 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 infinite impulse response (IIR) and finite impulse response (FIR) types. Whereas FIR filters are always stable, IIR filters have feedback loops that may become unstable and oscillate. The Z-transform provides a tool for analyzing stability issues of digital IIR filters. It is analogous to the Laplace transform, 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 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, wavelet transform,

filter bank In 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 ...

, non-linear (e.g., Wigner–Ville transform) and autoregressive 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 undesirable artifacts. Time-frequency analysis is usually used for analysis of non-stationary signals. For example, methods of fundamental frequency estimation, such as RAPT and PEFAC are based on windowed spectral analysis.

Wavelet

In numerical analysis and functional analysis, a discrete wavelet transform is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over

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 of time-frequency.

Empirical mode decomposition

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

Implementation

DSP algorithms may be run on general-purpose computers and

s. DSP algorithms are also implemented on purpose-built hardware such as application-specific integrated circuit (ASICs). Additional technologies for digital signal processing include more powerful general purpose microprocessors, graphics processing units,

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-programmable''. The FPGA configuration is generally specified using a hardware d ...

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 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 the collection and manipulation of digital data to produce meaningful information. Data processing is a form of ''information processing'', which is the modification (processing) of information in any manner detectable by an ...

, except DSP mathematical techniques (such as the DCT and FFT) 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. 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 designed to be configured by a customer or a designer after manufacturinghence the term '' field-programmable''. The FPGA configuration is generally specified using a hardware de ...

s may be used. For the most demanding applications or high-volume products,

ASIC An application-specific integrated circuit (ASIC ) is an integrated circuit (IC) chip customized for a particular use, rather than intended for general-purpose use, such as a chip designed to run in a digital voice recorder or a high-efficien ...

s might be designed specifically for the application. Parallel implementations of DSP algorithms, utilising multi-core CPU and many-core GPU architectures, are developed to improve the performances in terms of latency of these algorithms. is done by the computer's CPU rather than by DSP or outboard processing, which is done by additional third-party DSP chips located on extension cards or external hardware boxes or racks. Many digital audio workstations such as Logic Pro, Cubase, Digital Performer and Pro Tools LE use native processing. Others, such as Pro Tools HD, Universal Audio's UAD-1 and TC Electronic's Powercore use DSP processing.

Applications

General application areas for DSP include * Audio signal processing * Audio data compression e.g. MP3 * Video data compression * Computer graphics * Digital image processing * Photo manipulation * Speech processing * Speech recognition * Data transmission * Radar * Sonar * Financial signal processing * Economic forecasting * Seismology * Biomedicine * Weather forecasting Specific examples include speech coding and transmission in digital mobile phones, room correction of sound in hi-fi and sound reinforcement applications, analysis and control of industrial processes,

medical imaging Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to rev ...

such as CAT scans and MRI, audio crossovers and equalization,

digital synthesizer A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. This in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digit ...

s, and audio effects units.

Techniques

* Bilinear transform * Discrete Fourier transform *

Discrete-time Fourier transform In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function. The term ''discrete-time'' refers to the ...

* Filter design * Goertzel algorithm * Least-squares spectral analysis * LTI system theory * Minimum phase * s-plane * Transfer function * Z-transform

Computer engineering Computer engineering (CoE or CpE) is a branch of electrical engineering and computer science that integrates several fields of computer science and electronic engineering required to develop computer hardware and software. Computer engineers ...

* Computer science * Data compression * Dataflow programming * Discrete cosine transform *

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 ...

Fourier analysis In mathematics, Fourier analysis () is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Josep ...

Information theory Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...

* Machine learning * Real-time computing * Stream processing * Telecommunication * Time series * Wavelet

References

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