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Anamorphic Stretch Transform
An anamorphic stretch transform (AST) also referred to as warped stretch transform is a physics-inspired signal transform that emerged from time stretch dispersive Fourier transform. The transform can be applied to analog temporal signals such as communication signals, or to digital spatial data such as images. The transform reshapes the data in such a way that its output has properties conducive for data compression and analytics. The reshaping consists of warped stretching in the Fourier domain. The name "Anamorphic" is used because of the metaphoric analogy between the warped stretch operation and warping of images in anamorphosis and surrealist artworks. Operation principle An anamorphic stretch transform (AST) is a mathematical transformation in which analog or digital data is stretched and warped in a context-aware manner, such that it results in nonuniform Fourier domain sampling. The transformation is defined as: AST \left \ = \int_^\infty where \tilde_(\omega) is the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Transforms
This is a list of transforms in mathematics. Integral transforms *Abel transform * Aboodh transform * Bateman transform *Fourier transform ** Short-time Fourier transform **Gabor transform * Hankel transform * Hartley transform * Hermite transform *Hilbert transform ** Hilbert–Schmidt integral operator * Jacobi transform * Laguerre transform *Laplace transform ** Inverse Laplace transform **Two-sided Laplace transform ** Inverse two-sided Laplace transform * Laplace–Carson transform * Laplace–Stieltjes transform * Legendre transform * Linear canonical transform * Mellin transform ** Inverse Mellin transform ** Poisson–Mellin–Newton cycle * N-transform * Radon transform * Shehu transform * Stieltjes transformation * Sumudu transform * Wavelet transform (integral) * Weierstrass transform Discrete transforms * Binomial transform *Discrete Fourier transform, DFT **Fast Fourier transform, a popular implementation of the DFT *Discrete cosine transform **Modified discrete co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Stretch Dispersive Fourier Transform
Time stretch dispersive Fourier transform (TS-DFT), otherwise known as time-stretch transform (TST), temporal Fourier transform or photonic time-stretch (PTS) is a spectroscopy technique that uses optical dispersion instead of a grating or prism to separate the light wavelengths and analyze the optical spectrum in real-time. It employs group-velocity dispersion ( GVD) to transform the spectrum of a broadband optical pulse into a time stretched temporal waveform. It is used to perform Fourier transformation on an optical signal on a single shot basis and at high frame rates for real-time analysis of fast dynamic processes. It replaces a diffraction grating and detector array with a dispersive fiber and single-pixel detector, enabling ultrafast real-time spectroscopy and imaging. Its nonuniform variant, warped-stretch transform, realized with nonlinear group delay, offers variable-rate spectral domain sampling, as well as the ability to engineer the time-bandwidth product of the sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Compression
In information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information. Typically, a device that performs data compression is referred to as an encoder, and one that performs the reversal of the process (decompression) as a decoder. The process of reducing the size of a data file is often referred to as data compression. In the context of data transmission, it is called source coding: encoding is done at the source of the data before it is stored or transmitted. Source coding should not be confused with channel coding, for error detection and correction or line coding, the means for mapping data onto a sig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Analysis
Data analysis is the process of inspecting, Data cleansing, cleansing, Data transformation, transforming, and Data modeling, modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively. Data mining is a particular data analysis technique that focuses on statistical modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing mainly on business information. In statistical applications, data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and Statistical h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anamorphosis
Anamorphosis is a distorted projection that requires the viewer to occupy a specific vantage point, use special devices, or both to view a recognizable image. It is used in painting, photography, sculpture and installation, toys, and film special effects. The word is derived from the Greek prefix ''ana-'', meaning "back" or "again", and the word ''morphe'', meaning "shape" or "form". Extreme anamorphosis has been used by artists to disguise caricatures, erotic and scatological scenes, and other furtive images from a casual spectator, while revealing an undistorted image to the knowledgeable viewer. Types of projection There are two main types of anamorphosis: ''perspective'' (oblique) and ''mirror'' (catoptric). More complex anamorphoses can be devised using distorted lenses, mirrors, or other optical transformations. An oblique anamorphism forms an affine transformation of the subject. Early examples of Perspective (graphical), perspectival anamorphosis date to the Renaissa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surrealism
Surrealism is an art movement, art and cultural movement that developed in Europe in the aftermath of World War I in which artists aimed to allow the unconscious mind to express itself, often resulting in the depiction of illogical or dreamlike scenes and ideas. Its intention was, according to leader André Breton, to "resolve the previously contradictory conditions of dream and reality into an absolute reality, a super-reality", or ''surreality.'' It produced works of painting, writing, photography, Theatre of Cruelty, theatre, Surrealist cinema, filmmaking, Surrealist music, music, Surreal humour, comedy and other media as well. Works of Surrealism feature the element of surprise, unexpected juxtapositions and ''Non sequitur (literary device), non sequitur''. However, many Surrealist artists and writers regard their work as an expression of the philosophical movement first and foremost (for instance, of the "pure psychic automatic behavior, automatism" Breton speaks of in the fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Time–frequency Distribution
Bilinear time–frequency distributions, or quadratic time–frequency distributions, arise in a sub-field of signal analysis and signal processing called time–frequency signal processing, and, in the statistical analysis of time series data. Such methods are used where one needs to deal with a situation where the frequency composition of a signal may be changing over time; this sub-field used to be called time–frequency signal analysis, and is now more often called time–frequency signal processing due to the progress in using these methods to a wide range of signal-processing problems. Background Methods for analysing time series, in both signal analysis and time series analysis, have been developed as essentially separate methodologies applicable to, and based in, either the time or the frequency domain. A mixed approach is required in time–frequency analysis techniques which are especially effective in analyzing non-stationary signals, whose frequency distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog-to-digital Converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) 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 (signal processing), digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or Electric current, 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. There are several ADC hardware architecture, architectures. Due to the complexity and the need for precisely matched electronic component, components, all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both Analogue electronics, anal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Stretch Analog-to-digital Converter
The time-stretch analog-to-digital converter (TS-ADC), also known as the time-stretch enhanced recorder (TiSER), is an analog-to-digital converter (ADC) system that has the capability of digitizing very high Bandwidth (signal processing), bandwidth Signal (electrical engineering), signals that cannot be captured by conventional Electronics, electronic ADCs. Alternatively, it is also known as the photonic time-stretch (PTS) digitizer,J. Capmany and Dalma Novak, D. Novak, "Microwave photonics combines two worlds," ''Nature Photonics'' 1, 319-330 (2007)/ref> since it uses an Optics, optical Front-end and back-end, frontend. It relies on the process of time-stretch, which effectively slows down the analog signal in time (or compresses its bandwidth) before it can be digitized by a standard electronic ADC. Background There is a huge demand for very high-speed analog-to-digital converters (ADCs), as they are needed for Electronic test equipment, test and measurement equipment in laborat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Effective Number Of Bits
Effective number of bits (ENOB) is a measure of the real dynamic range of an analog-to-digital converter (ADC), digital-to-analog converter (DAC), or associated circuitry. Although the resolution of a converter may be specified by the number of bits used to represent the analog value, real circuits however are imperfect and introduce additional noise and distortion. Those imperfections reduce the number of bits of accuracy. The ENOB describes the effective resolution of a real converter in terms of the number of bits an ideal converter with the same resolution would have. ENOB is also used as a quality measure for other blocks such as sample-and-hold amplifiers. Thus analog blocks may be included in signal-chain calculations. The total ENOB of a chain of blocks is usually less than the ENOB of the worst block. Definition An often used definition for ENOB is, Equation 1. :\mathrm = \frac, where * ENOB is given in bits * SINAD (signal, noise, and distortion) is a power ratio indic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lossy Compression
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. Higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques. Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by N ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Stretch Transform
Phase stretch transform (PST) is a computational approach to signal and image processing. One of its utilities is for feature detection and classification.M. H. Asghari, and B. Jalali, "Edge detection in digital images using dispersive phase stretch", International Journal of Biomedical Imaging, Vol. 2015, Article ID 687819, pp. 1–6 (2015). PST is related to time stretch dispersive Fourier transform. It transforms the image by emulating propagation through a diffractive medium with engineered 3D dispersive property (refractive index). The operation relies on symmetry of the dispersion profile and can be understood in terms of dispersive eigenfunctions or stretch modes.B. Jalali and A. Mahjoubfar, "Tailoring Wideband Signals With a Photonic Hardware Accelerator", Proceedings of the IEEE, Vol. 103, No. 7, pp. 1071–1086 (2015). PST performs similar functionality as phase-contrast microscopy, but on digital images. PST can be applied to digital images and temporal (time se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
