Digital signal processing

Information about Digital signal processing

This article is about Digital signal processing. For Digital signal processor, see Digital signal processor.


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 and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, image processing, signal processing for communications, biomedical signal processing, etc.

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.

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).

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

Main article: Sampling (signal processing)
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 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").

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.

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.

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 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.

Applications

The main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology, and biomedicine. Specific examples are speech compression and transmission in digital mobile phones, room matching equalization 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.

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.

Techniques

Related fields

References

  • 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 (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

External links

Online books:
Digital systems
Logic gate | digital circuit | integrated circuit (IC)
Theory — boolean logic | digital signal processing | computer architecture
Applications — digital photography | digital audio | digital video
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Digital signal processing
Theory — Nyquist–Shannon sampling theorem, estimation theory, detection theory
Sub-fields — audio signal processing | control engineering | digital image processing | speech processing | statistical signal processing
Techniques — Discrete Fourier transform (DFT) | Discrete-time Fourier transform (DTFT) | bilinear transform | Z-transform, advanced Z-transform
Sampling — oversampling | undersampling | downsampling | upsampling | aliasing | anti-aliasing filter | sampling rate | Nyquist rate/frequency
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A digital signal processor (DSP) is a specialized microprocessor designed specifically for digital signal processing, generally in real-time computing.

Characteristics of typical Digital Signal Processors

  • Designed for real-time processing

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signal is any time-varying quantity. Signals are often scalar-valued functions of time (waveforms), but may be vector valued and may be functions of any other relevant independent variable.

The concept is broad, and hard to define precisely.
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A digital system is one that uses discrete values (often electrical voltages), representing numbers or non-numeric symbols such as letters or icons, for input, processing, transmission, storage, or display, rather than a continuous range of values (ie, as in an analog system).
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Analog signal processing is any signal processing conducted on analog signals by analog means. "Analog" indicates something that is mathematically represented as a set of continuous values. This differs from "digital" which uses a series of discrete quantities to represent signal.
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Signal processing is the analysis, interpretation and manipulation of signals. Signals of interest include sound, images, biological signals such as ECG, radar signals, and many others.
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Audio signal processing, sometimes referred to as audio processing, is the processing of a representation of auditory signals, or sound. The representation can be digital or analog.
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Speech signal processing refers to the acquisition, manipulation, storage, transfer and output of human utterances by a computer. The main goals are the recognition, synthesis and compression of human speech:

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Image processing is any form of information processing for which the input is an image, such as photographs or frames of video; the output is not necessarily an image, but can be for instance a set of features of the image.
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analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit, which converts continuous signals to discrete digital numbers. The reverse operation is performed by a digital-to-analog converter (DAC).
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digital-to-analog converter (DAC or D-to-A) is a device for converting a digital (usually binary) code to an analog signal (current, voltage or electric charge).

An analog-to-digital converter (ADC) performs the reverse operation.
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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 proceed through a well-defined series of successive states, eventually terminating in an
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Computer hardware is the physical part of a computer, including the digital circuitry, as distinguished from the computer software that executes within the hardware. The hardware of a computer is infrequently changed, in comparison with software and data, which are "soft" in the
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A digital signal processor (DSP) is a specialized microprocessor designed specifically for digital signal processing, generally in real-time computing.

Characteristics of typical Digital Signal Processors

  • Designed for real-time processing

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real-time computing (RToC) is the study of hardware and software systems which are subject to a "real-time constraint"—i.e., operational deadlines from event to system response.
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application-specific integrated circuit (ASIC) is an integrated circuit (IC) customized for a particular use, rather than intended for general-purpose use. For example, a chip designed solely to run a cell phone is an ASIC.
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field-programmable gate array is a semiconductor device containing programmable logic components called "logic blocks", and programmable interconnects. Logic blocks can be programmed to perform the function of basic logic gates such as AND, and XOR, or more complex combinational
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Time domain is a term used to describe the analysis of mathematical functions, or physical signals, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various separate instants in the case
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See also: Time domain
Frequency domain is a term used to describe the analysis of mathematical functions or signals with respect to frequency.
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Autocorrelation is a mathematical tool used frequently in signal processing for analysing functions or series of values, such as time domain signals. Informally, it is a measure of how well a signal matches a time-shifted version of itself, as a function of the amount of time shift.
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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. A wavelet transform is the representation of a function by wavelets.
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discrete Fourier transform (DFT), occasionally called the finite Fourier transform, is a transform for Fourier analysis of finite-domain discrete-time signals. As with most Fourier analyses, it expresses an input function in terms of a sum of sinusoidal components by determining
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frequency spectrum of the light. When all the visible frequencies are present in equal amounts, the effect is the "color" white, and the spectrum is a flat line. Therefore, flat-line spectrums in general are often referred to as white
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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
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In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous-time signal) to a sequence of samples (a discrete-time signal).
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computer is a machine which manipulates data according to a list of instructions.

Computers take numerous physical forms. The first devices that resemble modern computers date to the mid-20th century (around 1940 - 1941), although the computer concept and various machines
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analog-to-digital converter (abbreviated ADC, A/D or A to D) is an electronic integrated circuit, which converts continuous signals to discrete digital numbers. The reverse operation is performed by a digital-to-analog converter (DAC).
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discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers.
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quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively-small set of discrete symbols or integer values.
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equivalence class of an element a in X is the subset of all elements in X which are equivalent to a:
[a] =


The notion of equivalence classes is useful for constructing sets out of already constructed ones.
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The sampling rate, sample rate, or sampling frequency defines the number of samples per second (or per other unit) taken from a continuous signal to make a discrete signal. For time-domain signals, it can be measured in hertz (Hz).
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