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Encyclopedia > Digital signal processing

Digital signal processing (DSP) is the study of signals in a digital representation and the processing methods of these signals. DSP and analog signal processing are subfields of signal processing. DSP includes subfields like: audio signal processing, control engineering, digital image processing and speech processing. RADAR Signal processing and communications signal processing are two other important subfields of DSP. In information theory, a signal is the sequence of states of a communications channel that encodes a message. ... A digital system is one that uses discrete values (often electrical voltages), especially those representable as binary numbers, or non-numeric symbols such as letters or icons, for input, processing, transmission, storage, or display, rather than a continuous spectrum of values (ie, as in an analog system). ... Analog signal processing is any signal processing conducted on analog signals. ... Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ... This article or section does not cite its references or sources. ... Control engineering is the engineering discipline that focuses on the mathematical modelling systems of a diverse nature, analysing their dynamic behaviour, and using control theory to make a controller that will cause the systems to behave in a desired manner. ... Digital image processing is the use of computer algorithms to perform image processing on digital images. ... Speech processing is the study of speech signals and the processing methods of these signals. ... This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll. ...


Since the goal of DSP is usually to measure or filter continuous real-world analog signals, the first step is usually to convert the signal from an analog to a digital form, by using an analog to digital converter. Often, the required output signal is another analog output signal, which requires a digital to analog converter. This article or section should include material from AD converters In electronics, an analog-to-digital converter (abbreviated ADC, A/D, or A to D) is a device that converts continuous signals to discrete digital numbers. ... In electronics, a digital-to-analog converter (DAC or D-to-A) is a device for converting a digital (usually binary) code to an analogue signal (current, voltage or charges). ...


The algorithms required for DSP are sometimes performed using specialized computers, which make use of specialized microprocessors called digital signal processors (also abbreviated DSP). These process signals in real time and are generally purpose-designed application-specific integrated circuits (ASICs). When flexibility and rapid development are more important than unit costs at high volume, DSP algorithms may also be implemented using field-programmable gate arrays (FPGAs). In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ... Computer hardware is the physical part of a computer, including the digital circuitry, as distinguished from the computer software that executes within the hardware. ... A digital signal processor (DSP) is a specialized microprocessor designed specifically for digital signal processing, generally in real-time. ... It has been suggested that Real-time computing be merged into this article or section. ... This article does not cite any references or sources. ... An Altera Stratix II GX FPGA. A field-programmable gate array is a semiconductor device containing programmable logic components and programmable interconnects. ...

Contents

DSP domains

In DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, autocorrelation domain, and wavelet domains. They choose the domain in which to process a signal by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space. Time-domain is a term used to describe the analysis of mathematical functions, or real-life signals, with respect to time. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... A plot showing 100 random numbers with a hidden sine function, and an autocorrelation of the series on the bottom. ... A wavelet is a kind of mathematical function used to divide a given function into different frequency components and study each component with a resolution that matches its scale. ... In mathematics, the discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite-domain discrete-time signals. ... Familiar concepts associated with a frequency are colors, musical notes, radio/TV channels, and even the regular rotation of the earth. ... In statistics, the term cross-correlation is sometimes used to refer to the covariance cov(X, Y) between two random vectors X and Y, in order to distinguish that concept from the covariance of a random vector X, which is understood to be the matrix of covariances between the scalar...


Signal sampling

With the increasing use of computers the usage and need of digital signal processing has increased. In order to use an analog signal on a computer it must be digitized with an analog to digital converter (ADC). Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and discretization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the representative signal values are approximated by values from a finite set. In signal processing, sampling is the reduction of a continuous signal to a discrete signal. ... The NASA Columbia Supercomputer. ... This article or section should include material from AD converters In electronics, an analog-to-digital converter (abbreviated ADC, A/D, or A to D) is a device that converts continuous signals to discrete digital numbers. ... Discretization concerns the process of transferring continuous models and equations into discrete counterparts. ... Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ... In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element a in X is the subset of all elements in X which are equivalent to a: [a] = { x ∈ X | x ~ a } The notion of equivalence classes is useful for constructing sets out...


In order for a sampled analog signal to be exactly reconstructed, the Nyquist-Shannon sampling theorem must be satisfied. This theorem states that the sampling frequency must be greater than twice the bandwidth of the signal. In practice, the sampling frequency is often significantly more than twice the required bandwidth. The most common bandwidth scenarios are: DC - BWx ("baseband"); and Fc +/-BWx, a frequency band centered on a carrier frequency ("direct demodulation"). The Nyquist-Shannon sampling theorem is the fundamental theorem in the field of information theory, in particular telecommunications. ... The sampling frequency or sampling rate defines the number of samples per second taken from a continuous signal to make a discrete signal. ...


A digital to analog converter (DAC) is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient into digital control systems. In electronics, a digital-to-analog converter (DAC or D-to-A) is a device for converting a digital (usually binary) code to an analogue signal (current, voltage or charges). ... Digital control is a branch of control theory that uses digital computers to act as a system. ...


Time and space domains

The most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Filtering generally consists of some transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:

  • A "linear" filter is a linear transformation of input samples; other filters are "non-linear." Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination of different signals, the output is an equally weighted linear combination of the corresponding output signals.
  • A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.
  • A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.
  • Some filters are "stable", others are "unstable". A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter produces output which diverges.
  • A "finite impulse response" (FIR) filter uses only the input signal, while an "infinite impulse response" filter (IIR) uses both the input signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.

Most filters can be described in Z-domain (a superset of the frequency domain) by their transfer functions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response. The output of an FIR filter to any given input may be calculated by convolving the input signal with the impulse response. Filters can also be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. In mathematics, a linear transformation (also called linear map or linear operator) is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication. ... An adaptive filter is a digital filter that performs digital signal processing and can adapt its performance based on the input signal. ... A finite impulse response (FIR) filter is a type of a digital filter. ... IIR may stand for: infinite impulse response (a property of some types of electronic filter) This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... In mathematics, a recurrence relation, also known as a difference equation, is an equation which defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. ... In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0. ... The Impulse response from a simple audio system. ... In control theory the unit step response is the response of a dynamic system to the Heaviside step function. ... In mathematics and, in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. ... The Impulse response from a simple audio system. ... In mathematics, computing, linguistics, and related disciplines, an algorithm is a finite list of well-defined instructions for accomplishing some task that, given an initial state, will terminate in a defined end-state. ...


Frequency domain

Signals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency. Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared. In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...


The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to get information of which frequencies are present in the input signal and which are missing.


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 frequency components with smaller magnitude while retaining the order of magnitudes of frequency components. A cepstrum (pronounced ) is the result of taking the Fourier transform (FT) of the decibel spectrum as if it were a signal. ...


Applications

The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications and RADAR. Specific examples are speech compression and transmission in digital mobile phones, room matching equalisation of sound in Hifi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, computer-generated animations in movies, medical imaging such as CAT scans and MRI, image manipulation, high fidelity loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers. This article or section does not cite its references or sources. ... Audio compression can mean two things: Audio data compression - in which the amount of data in a recorded waveform is reduced for transmission. ... Digital image processing is the use of computer algorithms to perform image processing on digital images. ... Video compression refers to making a digital video signal use less data, without noticeably reducing the quality of the picture. ... Speech processing is the study of speech signals and the processing methods of these signals. ... Speech recognition (in many contexts also known as automatic speech recognition, computer speech recognition or erroneously as Voice Recognition) is the process of converting a speech signal to a sequence of words, by means of an algorithm implemented as a computer program. ... Digital communication, as opposed to analogue communication refers to all emerging communications and technologies via a digital platform usually combining text, graphics, sound, and video, utilising computer or mobile technology. ... This long range radar antenna, known as ALTAIR, is used to detect and track space objects in conjunction with ABM testing at the Ronald Reagan Test Site on the Kwajalein atoll. ... Speech coding is the compression of speech (into a code) for transmission with speech codecs that use audio signal processing and speech processing techniques. ... High Fidelity is also the title of a book by Nick Hornby and a film directed by Stephen Frears, based upon Hornbys book. ... A sound reinforcement system is an electromechanical system for accurately amplifying, reproducing, and sometimes recording audio, so that persons not near the original source may experience the sound as if they were. ... Modern weather predictions aid in timely evacuations and potentially save lives and property damage Weather map of Europe, 10 December 1887 Weather forecasting is the application of science and technology to predict the state of the atmosphere for a future time and a given location. ... Economic forecasting is the process of making predictions about the economy as a whole or in part. ... Seismology (from the Greek seismos = earthquake and logos = word) is the scientific study of earthquakes and the propagation of elastic waves through the Earth. ... Industrial processes are procedures involving chemical or mechanical steps to aid in the manufacture an item or items. ... The bouncing ball animation (below) consists of these 6 frames. ... Film is a term that encompasses individual motion pictures, the field of film as an art form, and the motion picture industry. ... Medical imaging designates the ensemble of techniques and processes used to create images of the human body (or parts thereof) for clinical purposes (medical procedures seeking to reveal, diagnose or examine disease) or medical science (including the study of normal anatomy and function). ... Binomial name Felis catus Linnaeus, 1758 Synonyms Felis lybica invalid junior synonym The cat (or domestic cat, house cat) is a small carnivorous mammal. ... The mri are a fictional alien species in the Faded Sun Trilogy of C.J. Cherryh. ... Computer graphics is a sub-field of computer science and is concerned with digitally synthesizing and manipulating visual content. ... Sound effects or audio effects are artificially created or enhanced sounds, or sound processes used to emphasize artistic or other content of movies, video games, music, or other media. ... Left: Rosa Hurricane, a heavy metal-style solid body guitar. ... An amplifier is a device which changes a small movement into a larger movement. ...


A further application is very low frequency (VLF) reception with a PC soundcard [1]. It is also used to analyse data in the fields of geophysics and seismology, petroleum exploration and exploitation, and neurophysiology. Very low frequency or VLF refers to radio frequencies (RF) in the range of 3 to 30 kHz. ... Neurophysiology is a part of physiology as a science, which is concerned with the study of the nervous system. ...


Implementation

Digital signal processing is often implemented using specialised micro processors such as the MC56000 and the TMS320. These often process data using fixed-point arithmetic, although some versions are available which use floating point arithmetic and are more powerful. For faster applications FPGAs might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and startup Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications such as flame scanning, a traditional slower processor such as a microcontroller can cope. A digital signal processor (DSP) is a specialized microprocessor designed specifically for digital signal processing, generally in real-time. ... It has been suggested that Binary scaling be merged into this article or section. ... A floating-point number is a digital representation for a number in a certain subset of the rational numbers, and is often used to approximate an arbitrary real number on a computer. ... A field-programmable gate array or FPGA is a gate array that can be reprogrammed after it is manufactured, rather than having its programming fixed during the manufacturing — a programmable logic device. ... The acronym ASIC, depending on context, may stand for: Application-specific integrated circuit ASIC programming language Australian Securities and Investments Commission This is a disambiguation page — a navigational aid which lists pages that might otherwise share the same title. ...


Techniques

In digital signal processing, the bilinear transform is a conformal mapping, often used to convert a transfer function of a linear, time-invariant (LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function of a linear, shift-invariant filter in the discrete-time domain... In mathematics, the discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite-domain discrete-time signals. ... Given a discrete set of real or complex numbers: (integers), the discrete-time Fourier transform (or DTFT) of is: // Its name implies that the {x[n]} sequence represents the values (aka samples) of a continuous-time function, , at discrete moments in time: , where is the sampling interval (in seconds), and... Filter design is the process of working out a filter (in the sense in which the term is used in signal processing, statistics, and applied mathematics), often a linear shift-invariant filter, which satisfies a set of requirements, some of which are contradicting. ... In electrical engineering, specifically in signal processing and control theory, LTI system theory investigates the response of a linear, time-invariant system to an arbitrary input signal. ... In control theory and signal processing, a linear, time-invariant system is minimum-phase if the system and its inverse are causal and stable. ... A transfer function is a mathematical representation of the relation between the input and output of a linear time-invariant system. ... In mathematics and signal processing, the Z-transform converts a discrete time domain signal, which is a sequence of real numbers, into a complex frequency domain representation. ... The Goertzel algorithm is a digital signal processing (DSP) technique for identifying frequency components of a signal, published by Dr. Gerald Goertzel in 1958. ... The S plane is a mathematical domain where, instead of viewing processes in the time domain modelled with time-based functions, they are viewed as equations in the frequency domain. ...

Related fields

Automatic control is the research area and theoretical base for mechanization and automation, employing methods from mathematics and engineering. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ... In computer science and information theory, data compression or source coding is the process of encoding information using fewer bits (or other information-bearing units) than an unencoded representation would use through use of specific encoding schemes. ... Electrical Engineers design power systems… … and complex electronic circuits. ... A bundle of optical fiber. ... Noise, Vibration, and Harshness, also known as Noise and Vibration, abbreviated to NVH and N&V respectively, is the name given to the field of measuring, and modifying, the noise and vibration characteristics of vehicles, particularly cars and trucks. ... Seismology (from the Greek seismos = earthquake and logos = word) is the scientific study of earthquakes and the propagation of elastic waves through the Earth. ... Copy of the original phone of Alexander Graham Bell at the Musée des Arts et Métiers in Paris Telecommunication is the transmission of signals over a distance for the purpose of communication. ...

References

  • Alan V. Oppenheim, Ronald W. Schafer, John R. Buck : Discrete-Time Signal Processing, Prentice Hall, ISBN 0-13-754920-2
  • Richard G. Lyons: Understanding Digital Signal Processing, Prentice Hall, ISBN 0-13-108989-7
  • Jonathan (Y) Stein, Digital Signal Processing, a Computer Science Perspective, Wiley, ISBN 0-471-29546-9
  • Sen M. Kuo, Woon-Seng Gan: Digital Signal Processors: Architectures, Implementations, and Applications, Prentice Hall, ISBN 0-13-035214-4
  • Bernard Mulgrew, Peter Grant, John Thompson: Digital Signal Processing - Concepts and Applications, Palgrave Macmillan, ISBN 0-333-96356-3
  • Steven W. Smith: Digital Signal Processing - A Practical Guide for Engineers and Scientists, Newnes, ISBN 0-7506-7444-X
  • Paul A. Lynn, Wolfgang Fuerst: Introductory Digital Signal Processing with Computer Applications, John Wiley & Sons, ISBN 0-471-97984-8
  • James D. Broesch: Digital Signal Processing Demystified, Newnes, ISBN 1-878707-16-7
  • John G. Proakis, Dimitris Manolakis: Digital Signal Processing - Principles, Algorithms and Applications, Pearson, ISBN 0-13-394289-9
  • Hari Krishna Garg: Digital Signal Processing Algorithms, CRC Press, ISBN 0-8493-7178-3
  • P. Gaydecki: Foundations Of Digital Signal Processing: Theory, Algorithms And Hardware Design, Institution of Electrical Engineers, ISBN 0-85296-431-5
  • Paul M. Embree, Damon Danieli: C++ Algorithms for Digital Signal Processing, Prentice Hall, ISBN 0-13-179144-3
  • Anthony Zaknich: Neural Networks for Intelligent Signal Processing, World Scientific Pub Co Inc, ISBN 981-238-305-0
  • Vijay Madisetti, Douglas B. Williams: The Digital Signal Processing Handbook, CRC Press, ISBN 0-8493-8572-5
  • Stergios Stergiopoulos: Advanced Signal Processing Handbook: Theory and Implementation for Radar, Sonar, and Medical Imaging Real-Time Systems, CRC Press, ISBN 0-8493-3691-0
  • Joyce Van De Vegte: Fundamentals of Digital Signal Processing, Prentice Hall, ISBN 0-13-016077-6
  • Ashfaq Khan: Digital Signal Processing Fundamentals, Charles River Media, ISBN 1-58450-281-9
  • Jonathan M. Blackledge, Martin Turner: Digital Signal Processing: Mathematical and Computational Methods, Software Development and Applications, Horwood Publishing, ISBN 1-898563-48-9
  • Bimal Krishna, K. Y. Lin, Hari C. Krishna: Computational Number Theory & Digital Signal Processing, CRC Press, ISBN 0-8493-7177-5
  • Doug Smith: Digital Signal Processing Technology: Essentials of the Communications Revolution, American Radio Relay League, ISBN 0-87259-819-5
  • Henrique S. Malvar: Signal Processing with Lapped Transforms, Artech House Publishers, ISBN 0-89006-467-9
  • Charles A. Schuler: Digital Signal Processing: A Hands-On Approach, McGraw-Hill, ISBN 0-07-829744-3
  • James H. McClellan, Ronald W. Schafer, Mark A. Yoder: Signal Processing First, Prentice Hall, ISBN 0-13-090999-8
  • Artur Krukowski, Izzet Kale: DSP System Design: Complexity Reduced Iir Filter Implementation for Practical Applications, Kluwer Academic Publishers, ISBN 1-4020-7558-8
  • John G. Proakis: A Self-Study Guide for Digital Signal Processing, Prentice Hall, ISBN 0-13-143239-7

Professor Alan V. Oppenheim Alan V. Oppenheim is a Ford Professor of Engineering at the MITs Department of Electrical Engineering and Computer Science. ... Ronald Schafer is an electrical engineer notable for his contributions to digital signal processing. ... Biography James H. McClellan is a professor at the Georgia Institute of Technology. ... Ronald Schafer is an electrical engineer notable for his contributions to digital signal processing. ...

External links


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