Signal processing

Last updated
The signal on the left looks like noise, but the signal processing technique known as the Fourier transform (right) shows that it contains five well-defined frequency components.

Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as sound, images, and scientific measurements. [1] Signal processing techniques can be used to improve transmission, storage efficiency and subjective quality and to also emphasize or detect components of interest in a measured signal. [2]

History

According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. [3]

In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. [4] The paper laid the groundwork for later development of information communication systems and the processing of signals for transmission. [5]

Signal processing matured and flourished in the 1960s and 1970s, and digital signal processing became widely used with specialized digital signal processor chips in the 1980s. [5]

Categories

Analog

Analog signal processing is for signals that have not been digitized, as in most 20th-century radio, telephone, radar, and television systems. This involves linear electronic circuits as well as nonlinear ones. The former are, for instance, passive filters, active filters, additive mixers, integrators, and delay lines. Nonlinear circuits include compandors, multipliers (frequency mixers, voltage-controlled amplifiers), voltage-controlled filters, voltage-controlled oscillators, and phase-locked loops.

Continuous time

Continuous-time signal processing is for signals that vary with the change of continuous domain (without considering some individual interrupted points).

The methods of signal processing include time domain, frequency domain, and complex frequency domain. This technology mainly discusses the modeling of linear time-invariant continuous system, integral of the system's zero-state response, setting up system function and the continuous time filtering of deterministic signals

Discrete time

Discrete-time signal processing is for sampled signals, defined only at discrete points in time, and as such are quantized in time, but not in magnitude.

Analog discrete-time signal processing is a technology based on electronic devices such as sample and hold circuits, analog time-division multiplexers, analog delay lines and analog feedback shift registers. This technology was a predecessor of digital signal processing (see below), and is still used in advanced processing of gigahertz signals.

The concept of discrete-time signal processing also refers to a theoretical discipline that establishes a mathematical basis for digital signal processing, without taking quantization error into consideration.

Digital

Digital signal processing is the processing of digitized discrete-time sampled signals. Processing is done by general-purpose computers or by digital circuits such as ASICs, field-programmable gate arrays or specialized digital signal processors (DSP chips). Typical arithmetical operations include fixed-point and floating-point, real-valued and complex-valued, multiplication and addition. Other typical operations supported by the hardware are circular buffers and lookup tables. Examples of algorithms are the fast Fourier transform (FFT), finite impulse response (FIR) filter, Infinite impulse response (IIR) filter, and adaptive filters such as the Wiener and Kalman filters.

Nonlinear

Nonlinear signal processing involves the analysis and processing of signals produced from nonlinear systems and can be in the time, frequency, or spatio-temporal domains. [6] [7] Nonlinear systems can produce highly complex behaviors including bifurcations, chaos, harmonics, and subharmonics which cannot be produced or analyzed using linear methods.

Polynomial signal processing is a type of non-linear signal processing, where polynomial systems may be interpreted as conceptually straight forward extensions of linear systems to the non-linear case. [8]

Statistical

Statistical signal processing is an approach which treats signals as stochastic processes, utilizing their statistical properties to perform signal processing tasks. [9] Statistical techniques are widely used in signal processing applications. For example, one can model the probability distribution of noise incurred when photographing an image, and construct techniques based on this model to reduce the noise in the resulting image.

Application fields

In communication systems, signal processing may occur at:

Related Research Articles

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 of compressions and rarefactions. The energy contained in audio signals is typically measured in decibels. As audio signals may be represented in either digital or analog format, processing may occur in either domain. Analog processors operate directly on the electrical signal, while digital processors operate mathematically on its digital representation.

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable 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.

In electronics, an analog-to-digital converter 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. An ADC may also provide an isolated measurement such as an electronic device that converts an input analog voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities.

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals.

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one recorded by a seismograph or heart monitor. Generally, wavelets are intentionally crafted to have specific properties that make them useful for signal processing.

System analysis in the field of electrical engineering that characterizes electrical systems and their properties. System analysis can be used to represent almost anything from population growth to audio speakers; electrical engineers often use it because of its direct relevance to many areas of their discipline, most notably signal processing, communication systems and control systems.

Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which are contradictory. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful.

In signal processing, a signal is a function that conveys information about a phenomenon. In electronics and telecommunications, it refers to any time varying voltage, current, or electromagnetic wave that carries information. A signal may also be defined as an observable change in a quality such as quantity.

Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input. For a linear system, doubling the amplitude of the input will double the amplitude of the output, and summing two inputs produces an output that is the sum of the two corresponding outputs to the individual inputs. In addition, if the system is time-invariant, then the frequency response also will not vary with time, and injecting a sine wave into the system at a given frequency will make the system respond at that same frequency with a certain magnitude and a certain phase angle relative to the input. Thus for LTI systems, the frequency response can be seen as applying the system's transfer function to a purely imaginary number argument representing the frequency of the sinusoidal excitation.

In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.

In mathematics, a time series is a series of data points indexed in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

Direct digital synthesis (DDS) is a method employed by frequency synthesizers used for creating arbitrary waveforms from a single, fixed-frequency reference clock. DDS is used in applications such as signal generation, local oscillators in communication systems, function generators, mixers, modulators, sound synthesizers and as part of a digital phase-locked loop.

In signal processing, a filter bank is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called analysis ; the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called synthesis, meaning reconstitution of a complete signal resulting from the filtering process.

The following outline is provided as an overview of and topical guide to electrical engineering.

Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components and interconnections that, in analysis, can be considered to exist at a single point. These components can be in discrete packages or part of an integrated circuit.

In signal processing, a nonlinearfilter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals R and S for two input signals r and s separately, but does not always output αR + βS when the input is a linear combination αr + βs.

Sample-rate conversion is the process of changing the sampling rate of a discrete signal to obtain a new discrete representation of the underlying continuous signal. Application areas include image scaling and audio/visual systems, where different sampling rates may be used for engineering, economic, or historical reasons.

Ali Naci Akansu is a Turkish-American Professor of electrical & computer engineering and scientist in applied mathematics. He is best known for his seminal contributions to the theory and applications of linear subspace methods including sub-band and wavelet transforms, particularly the binomial QMF and the development of framework to design statistically optimized filter bank, which he published in 1990 and 1991, respectively.

In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics.

Multidimensional Digital Pre-distortion (MDDPD), often referred to as multiband digital pre-distortion (MBDPD), is a subset of digital predistortion (DPD) that enables DPD to be applied to signals (channels) that cannot or do not pass through the same digital pre-distorter but do concurrently pass through the same nonlinear system. Its ability to do so comes from the portion of multidimensional signal theory that deals with one dimensional discrete time vector input - 1-D discrete time vector output systems as defined in Multidimensional Digital Signal Processing. The first paper in which it found application was in 1991 as seen here. None of the applications of MDDPD are able to make use of the linear shift invariant (LSI) system properties as by definition they are nonlinear and not shift-invariant although they are often approximated as shift-invariant (memoryless).

References

1. Sengupta, Nandini; Sahidullah, Md; Saha, Goutam (August 2016). "Lung sound classification using cepstral-based statistical features". Computers in Biology and Medicine. 75 (1): 118–129. doi:10.1016/j.compbiomed.2016.05.013. PMID   27286184.
2. Alan V. Oppenheim and Ronald W. Schafer (1989). Discrete-Time Signal Processing. Prentice Hall. p. 1. ISBN   0-13-216771-9.
3. Oppenheim, Alan V.; Schafer, Ronald W. (1975). Digital Signal Processing. Prentice Hall. p. 5. ISBN   0-13-214635-5.
4. "A Mathematical Theory of Communication – CHM Revolution". Computer History. Retrieved 2019-05-13.
5. Fifty Years of Signal Processing: The IEEE Signal Processing Society and its Technologies, 1948–1998. The IEEE Signal Processing Society. 1998.
6. Billings, S. A. (2013). Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains. Wiley. ISBN   978-1119943594.
7. Slawinska, J., Ourmazd, A., and Giannakis, D. (2018). "A New Approach to Signal Processing of Spatiotemporal Data". 2018 IEEE Statistical Signal Processing Workshop (SSP). IEEE Xplore. pp. 338–342. doi:10.1109/SSP.2018.8450704. ISBN   978-1-5386-1571-3. S2CID   52153144.CS1 maint: uses authors parameter (link)
8. V. John Mathews; Giovanni L. Sicuranza. Polynomial Signal Processing. Wiley. ISBN   978-0-471-03414-8.
9. Scharf, Louis L. (1991). Statistical signal processing: detection, estimation, and time series analysis. Boston: Addison–Wesley. ISBN   0-201-19038-9. OCLC   61160161.
10. Sarangi, Susanta; Sahidullah, Md; Saha, Goutam (September 2020). "Optimization of data-driven filterbank for automatic speaker verification". Digital Signal Processing. 104: 102795. arXiv:. doi:10.1016/j.dsp.2020.102795. S2CID   220665533.
11. Anastassiou, D. (2001). "Genomic signal processing". IEEE Signal Processing Magazine. IEEE. 18 (4): 8–20. doi:10.1109/79.939833.
12. Patrick Gaydecki (2004). Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design. IET. pp. 40–. ISBN   978-0-85296-431-6.
13. Shlomo Engelberg (8 January 2008). Digital Signal Processing: An Experimental Approach. Springer Science & Business Media. ISBN   978-1-84800-119-0.
14. Boashash, Boualem, ed. (2003). Time frequency signal analysis and processing a comprehensive reference (1 ed.). Amsterdam: Elsevier. ISBN   0-08-044335-4.
15. Stoica, Petre; Moses, Randolph (2005). Spectral Analysis of Signals (PDF). NJ: Prentice Hall.
16. Peter J. Schreier; Louis L. Scharf (4 February 2010). Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals. Cambridge University Press. ISBN   978-1-139-48762-7.
17. Max A. Little (13 August 2019). Machine Learning for Signal Processing: Data Science, Algorithms, and Computational Statistics. OUP Oxford. ISBN   978-0-19-102431-3.
18. Steven B. Damelin; Willard Miller, Jr (2012). The Mathematics of Signal Processing. Cambridge University Press. ISBN   978-1-107-01322-3.
19. Daniel P. Palomar; Yonina C. Eldar (2010). Convex Optimization in Signal Processing and Communications. Cambridge University Press. ISBN   978-0-521-76222-9.