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Signal Transfer Function
The signal transfer function (SiTF) is a measure of the signal output versus the signal input of a system such as an infrared system or sensor. There are many general applications of the SiTF. Specifically, in the field of image analysis, it gives a measure of the noise of an imaging system, and thus yields one assessment of its performance. SiTF evaluation In evaluating the SiTF curve, the signal input and signal output are measured differentially; meaning, the differential of the input signal and differential of the output signal are calculated and plotted against each other. An operator, using computer software, defines an arbitrary area, with a given set of data points, within the signal and background regions of the output image of the infrared sensor, i.e. of the unit under test (UUT), (see "Half Moon" image below). The average signal and background are calculated by averaging the data of each arbitrarily defined region. A second order polynomial curve is fitted to the ...
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Signal (electrical Engineering)
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' includes audio, video, speech, image, sonar, and radar as examples of signal. A signal may also be defined as observable change in a quantity over space or time (a time series), even if it does not carry information. In nature, signals can be actions done by an organism to alert other organisms, ranging from the release of plant chemicals to warn nearby plants of a predator, to sounds or motions made by animals to alert other animals of food. Signaling occurs in all organisms even at cellular levels, with cell signaling. Signaling theory, in evolutionary biology, proposes that a substantial driver for evolution is the ability of animals to communicate with each other by developing ways of signaling. In human engineering, signals are typi ...
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Signal To Noise Ratio (imaging)
Signal-to-noise ratio (SNR) is used in imaging to characterize image quality. The sensitivity of a (digital or film) imaging system is typically described in the terms of the signal level that yields a threshold level of SNR. Industry standards define sensitivity in terms of the ISO film speed equivalent, using SNR thresholds (at average scene luminance) of 40:1 for "excellent" image quality and 10:1 for "acceptable" image quality. SNR is sometimes quantified in decibels (dB) of signal power relative to noise power, though in the imaging field the concept of "power" is sometimes taken to be the power of a voltage signal proportional to optical power; so a 20 dB SNR may mean either 10:1 or 100:1 optical power, depending on which definition is in use. Definition of SNR Traditionally, SNR is defined to be the ratio of the average signal value \mu_\mathrm to the standard deviation of the signal \sigma_\mathrm: : \mathrm = \frac when the signal is an optical intensity, ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. 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. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ...
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Signal To Noise Ratio (imaging)
Signal-to-noise ratio (SNR) is used in imaging to characterize image quality. The sensitivity of a (digital or film) imaging system is typically described in the terms of the signal level that yields a threshold level of SNR. Industry standards define sensitivity in terms of the ISO film speed equivalent, using SNR thresholds (at average scene luminance) of 40:1 for "excellent" image quality and 10:1 for "acceptable" image quality. SNR is sometimes quantified in decibels (dB) of signal power relative to noise power, though in the imaging field the concept of "power" is sometimes taken to be the power of a voltage signal proportional to optical power; so a 20 dB SNR may mean either 10:1 or 100:1 optical power, depending on which definition is in use. Definition of SNR Traditionally, SNR is defined to be the ratio of the average signal value \mu_\mathrm to the standard deviation of the signal \sigma_\mathrm: : \mathrm = \frac when the signal is an optical intensity, ...
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Minimum Resolvable Contrast
Minimum resolvable contrast (MRC) is a subjective measure of a visible spectrum sensor’s or camera's sensitivity and ability to resolve data. A snapshot image of a series of three bar targets of selected spatial frequencies and various contrast coatings captured by the unit under test (UUT) is used to determine the MRC of the UUT, i.e. the visible spectrum camera or sensor. A trained observer selects the smallest target resolvable at each contrast level. Typically, specialized computer software collects the inputted data of the observer and provides a graph of contrast v.s. spatial frequency at a given luminance level. A first order polynomial is fitted to the data and an MRC curve of spatial frequency versus contrast is generated.Electro Optical Industries, Inc. (2005) "EO TestLab Methodology". In ''Education/Ref''. See also * Distortion * Image resolution * Integrating sphere * Minimum resolvable temperature difference Minimum resolvable temperature difference (MRTD) is ...
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Power Spectral Density
The power spectrum S_(f) of a time series x(t) describes the distribution of power into frequency components composing that signal. According to Fourier analysis, any physical signal can be decomposed into a number of discrete frequencies, or a spectrum of frequencies over a continuous range. The statistical average of a certain signal or sort of signal (including noise) as analyzed in terms of its frequency content, is called its spectrum. When the energy of the signal is concentrated around a finite time interval, especially if its total energy is finite, one may compute the energy spectral density. More commonly used is the power spectral density (or simply power spectrum), which applies to signals existing over ''all'' time, or over a time period large enough (especially in relation to the duration of a measurement) that it could as well have been over an infinite time interval. The power spectral density (PSD) then refers to the spectral energy distribution that would be ...
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Noise Equivalent Temperature Difference
Noise-equivalent temperature (NET) is a measure of the sensitivity of a detector of thermal radiation in the infrared, terahertz or microwave portions of the electromagnetic spectrum. It is the amount of incident signal temperature that would be needed to match the internal noise of the detector such that the signal-to-noise ratio is equal to one. Often the spectrum of the NET is reported as a temperature ''per root bandwidth''. A detector that measures power is often interested in the analogous noise-equivalent power (NEP). If a relation between intensity and temperature is well defined over the passband, as in the case of a blackbody, then the NET simply scales with the NEP. If a detector is limited by either shot noise or Johnson noise then the NET can be decreased by using an increased integration time. The NET of flicker noise limited detectors can not be reduced by increased integration time. Typically uncooled bolometric detectors have NET figures of 30-200 mK. Co ...
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Minimum Resolvable Temperature Difference
Minimum resolvable temperature difference (MRTD) is a measure for assessing the performance of infrared cameras, and is inversely proportional to the modulation transfer function. Typically, an operator is asked to assess the minimum temperature difference at which a 4-bar target can be resolved. This minimum difference will change with the spatial frequency of the bar target used. A curve of MRTD against spatial frequency is obtained which characterises the performance of the imaging system. Modern infrared imaging systems can have low spatial frequency MRTDs of tens of millikelvins. Manual test A manual subjective test is implemented to determine the MRTD. An operator uses a series of 4-bar targets of different spatial frequencies. For each target he/she adjusts the blackbody, (source of Infrared radiation), temperature up and down until the pattern is "just resolvable." The positive and negative temperature differences are stored into a two dimensional array. The correspon ...
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Distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal representing sound or a video signal representing images, in an electronic device or communication channel. Distortion is usually unwanted, and so engineers strive to eliminate or minimize it. In some situations, however, distortion may be desirable. For example, in noise reduction systems like the Dolby system, an audio signal is deliberately distorted in ways that emphasize aspects of the signal that are subject to electrical noise, then it is symmetrically "undistorted" after passing through a noisy communication channel, reducing the noise in the received signal. Distortion is also used as a musical effect, particularly with electric guitars. The addition of noise or other outside signals (hum, interference) is not considered di ...
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Optical Transfer Function
The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are captured or transmitted. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations. Either transfer function specifies the response to a periodic sine-wave pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the Fourier transform of the point spread function (PSF, that is, the impulse response of the optics, the image of a point source). As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmet ...
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Edward Aboufadel
Edward F. Aboufadel is an American mathematician currently Professor at Grand Valley State University and an Elected Fellow of the American Association for the Advancement of Science. Education He earned his B.S at Michigan State University in 1986 and his PhD at Rutgers University in 1992 under the supervision of Jane Cronin Scanlon. Research His interests are wavelets A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the num ... and data sets and 3D printing. His highest cited paper is "Discovering wavelets"E Aboufadel, S Schlicker. Discovering wavelets. 2011. John Wiley & Sons. Publications *Edward Aboufadel, David Austin. A new method for computing the mean center of population of the United States. 58:1. 65–69. The Professional Geographer. 2006. *Merle C Potter, Jack Leonard Goldberg, ...
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Least Squares
The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting. When the problem has substantial uncertainties in the independent variable (the ''x'' variable), then simple regression and least-squares methods have problems; in such cases, the methodology required for fitting errors-in-variables models may be considered instead of that for least squares. Least squares problems fall into two categories: linear or ordinary least squares and nonlinear least squares, depending on whether or not the residuals are linear in all unknowns. The linear least-squares problem occurs in statistical regressio ...
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