Information On digital signal processing

Digital signal processing (DSP is concerned with the representation of signal (electronics) by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing DSP includes subfields like: audio signal processing and speech signal processing sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing signal processing for communications, control of systems, biomedical signal processing, seismic data processing, etc. The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by samplingit using an analog-to-digital converter (ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analog converter (DAC). Even if this process is more complex than analog processing and has a discrete signal the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection in transmission as well as data compression lt;/ref> DSP algorithm have long been run on standard computers, on specialized processors called digital signal processor (DSPs), or on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessor , field-programmable gate array (FPGAs), Digital Signal Controller (mostly for industrial apps such as motor control), and stream processing among others.lt;/ref>

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.

Signal sampling

With the increasing use of computer the usage of and need for 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. Sampling is usually carried out in two stages, discretization and Quantization (signal processing) In the discretization stage, the space of signals is partitioned into equivalence class s and quantization 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. 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 of the signal. In practice, the sampling frequency is often significantly more than twice the required bandwidth. A digital-to-analog converter is used to convert the digital signal back to analog. The use of a digital computer is a key ingredient in digital control

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. Digital filter ng generally consists of some linear 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 filter 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 can produce an output that grows without bounds, with bounded or even zero input. * A "finite impulse response" (Finite impulse response filter uses only the input signals, 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. Filters can be represented by block diagrams which can then be used to derive a sample processing algorithm to implement the filter using hardware instructions. A filter may also be described as a difference equation a collection of Zero (complex analysis) and pole (complex analysis) or, if it is an FIR filter, an impulse response or step response The output of a digital filter to any given input may be calculated by convolution the input signal with the impulse response

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. 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. In addition to frequency information, phase information is often needed. This can be obtained from the fourier transform. With some applications, how the phase varies with frequency can be a significant consideration. Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filter . 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. Frequency domain analysis is also called spectrum-or spectral analysis

Z-domain analysis

Whereas analog filters are usually analysed on the Laplace Transform digital filters are analysed on the z-plane or z-domain in terms of z-transform . Most filters can be described in Z-domain (a complex number superset of the frequency domain) by their transfer function . A filter may be analysed in the z-domain by its characteristic collection of Zero (complex analysis) and pole (complex analysis) .

Applications

The main applications of DSP are audio signal processing audio compression digital image processing video compression speech processing speech recognition digital communication , RADAR SONAR seismology, and biomedicine. Specific examples are speech compression and transmission in digital mobile phone , room matching equalization of sound in Hifi and sound reinforcement applications, weather forecasting economic forecasting seismology data processing, analysis and control of industrial process s, computer-generated animation in Film , medical imaging such as CAT scans and MRI MP3 compression, computer graphics high fidelity loudspeaker crossovers and equalization, and sound effect for use with electric guitar amplifiers

Implementation

Digital signal processing is often implemented using Digital signal processor such as the Motorola 56000 the TMS320 or the Super Harvard Architecture Single-Chip Computer 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 FPGA lt;/ref> might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc For faster applications with vast usage, Application-specific integrated circuit might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also a growing number of DSP applications are now being implemented on Embedded Systems using powerful PCs with a Multi-core processor

Techniques

Related fields

* Analog signal processing * Automatic control * Computer Engineering * Computer Science * Data compression * Dataflow programming * Electrical engineering * Information theory * Telecommunication * Machine Learning * Stream processing * Wavelet * Fourier Analysis * Time series

References

Further reading

*Alan V Oppenheim Ronald W Schafer John R. Buck : Discrete-Time Signal Processing Prentice Hall, ISBN 0-13-754920-2 *Boaz Porat: A Course in Digital Signal Processing Wiley, ISBN 0471149616 *Richard G. Lyons: Understanding Digital Signal Processing Prentice Hall, ISBN 0-13-108989-7 *Jonathan Yaakov 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 * Gibson, John. “Spectral Delay as a Compositional Resource.” http://cec.concordia.ca/econtact/11_4/Gibson_spectraldelay.html eContact! 11.4 — Toronto Electroacoustic Symposium 2009 (TES) / Symposium Électroacoustique 2009 de Toronto (December 2009). Montréal: Canadian Electroacoustic Community *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
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