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S Transform
''S'' transform as a time–frequency distribution was developed in 1994 for analyzing geophysics data.Stockwell, RG (1999). ''S''-transform analysis of gravity wave activity from a small scale network of airglow imagers. PhD thesis, University of Western Ontario, London, Ontario, Canada. In this way, the ''S'' transform is a generalization of the short-time Fourier transform (STFT), extending the continuous wavelet transform and overcoming some of its disadvantages. For one, modulation sinusoids are fixed with respect to the time axis; this localizes the scalable Gaussian window dilations and translations in ''S'' transform. Moreover, the ''S'' transform doesn't have a cross-term problem and yields a better signal clarity than Gabor transform. However, the ''S'' transform has its own disadvantages: the clarity is worse than Wigner distribution function and Cohen's class distribution function. A fast ''S'' transform algorithm was invented in 2010. It reduces the computational compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-time Fourier Transform
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reflection Seismology
Reflection seismology (or seismic reflection) is a method of exploration geophysics that uses the principles of seismology to estimate the properties of the Earth's subsurface from reflection (physics), reflected seismic waves. The method requires a controlled seismic source of energy, such as dynamite or Tovex blast, a specialized Seismic source#Air gun, air gun or a seismic vibrator. Reflection seismology is similar to sonar and acoustic location, echolocation. History Reflections and refractions of seismic waves at geologic Interface (matter), interfaces within the Earth were first observed on recordings of earthquake-generated seismic waves. The basic model of the Earth's deep interior is based on observations of earthquake-generated seismic waves transmitted through the Earth's interior (e.g., Mohorovičić, 1910). The use of human-generated seismic waves to map in detail the geology of the upper few kilometers of the Earth's crust followed shortly thereafter and has deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integral Transforms
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space. The transformed function can generally be mapped back to the original function space using the ''inverse transform''. General form An integral transform is any transform ''T'' of the following form: :(Tf)(u) = \int_^ f(t)\, K(t, u)\, dt The input of this transform is a function ''f'', and the output is another function ''Tf''. An integral transform is a particular kind of mathematical operator. There are numerous useful integral transforms. Each is specified by a choice of the function K of two variables, that is called the kernel or nucleus of the transform. Some kernels have an associated ''inverse kernel'' K^( u,t ) which (roughly speaking) yields an inverse transform: : ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of Earthquake Engineering
The ''Bulletin of Earthquake Engineering'' is a bimonthly peer-reviewed scientific journal published by Springer Science+Business Media on behalf of the European Association for Earthquake Engineering. It covers all aspects of earthquake engineering. It was established in 2003 and the editor-in-chief is Atilla Ansal ( Ozyegin University). Abstracting and indexing This journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a type of journal ranking. Journals with higher impact factor values are considered more prestigious or important within their field. The Impact Factor of a journa ... of 3.827. References External links * Earthquake engineering Springer Science+Business Media academic journals Quarterly journals English-language journals Engineering journals Academic journals established in 2003 {{enginee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-time Fourier Transform
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Seismology
Seismology (; from Ancient Greek σεισμός (''seismós'') meaning "earthquake" and -λογία (''-logía'') meaning "study of") is the scientific study of earthquakes (or generally, quakes) and the generation and propagation of elastic waves through planetary bodies. It also includes studies of the environmental effects of earthquakes such as tsunamis; other seismic sources such as volcanoes, plate tectonics, glaciers, rivers, oceanic microseisms, and the atmosphere; and artificial processes such as explosions. Paleoseismology is a related field that uses geology to infer information regarding past earthquakes. A recording of Earth's motion as a function of time, created by a seismograph is called a seismogram. A seismologist is a scientist who works in basic or applied seismology. History Scholarly interest in earthquakes can be traced back to antiquity. Early speculations on the natural causes of earthquakes were included in the writings of Thales of Miletu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiresolution Analysis
A multiresolution analysis (MRA) or multiscale approximation (MSA) is the design method of most of the practically relevant discrete wavelet transforms (DWT) and the justification for the algorithm of the fast wavelet transform (FWT). It was introduced in this context in 1988/89 by Stephane Mallat and Yves Meyer and has predecessors in the microlocal analysis in the theory of differential equations (the ''ironing method'') and the pyramid methods of image processing as introduced in 1981/83 by Peter J. Burt, Edward H. Adelson anJames L. Crowley Definition A multiresolution analysis of the Lebesgue space L^2(\mathbb) consists of a sequence of nested subspaces ::\\subset \dots\subset V_1\subset V_0\subset V_\subset\dots\subset V_\subset V_\subset\dots\subset L^2(\R) that satisfies certain self-similarity relations in time-space and scale-frequency, as well as completeness and regularity relations. * ''Self-similarity'' in ''time'' demands that each subspace ''Vk'' is in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Wavelet Transform
In mathematics, the continuous wavelet transform (CWT) is a formal (i.e., non-numerical) tool that provides an overcomplete representation of a signal by letting the translation and scale parameter of the wavelets vary continuously. Definition The continuous wavelet transform of a function x(t) at a scale a\in\mathbb and translational value b\in\mathbb is expressed by the following integral :X_w(a,b)=\frac \int_^\infty x(t)\overline\psi\left(\frac\right)\,\mathrmt where \psi(t) is a continuous function in both the time domain and the frequency domain called the mother wavelet and the overline represents operation of complex conjugate. The main purpose of the mother wavelet is to provide a source function to generate the daughter wavelets which are simply the translated and scaled versions of the mother wavelet. To recover the original signal x(t), the first inverse continuous wavelet transform can be exploited. :x(t)=C_\psi^\int_^\int_^ X_w(a,b)\frac\tilde\psi\left(\frac\righ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Resonance Imaging
Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to generate pictures of the anatomy and the physiological processes inside the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves to form images of the organs in the body. MRI does not involve X-rays or the use of ionizing radiation, which distinguishes it from computed tomography (CT) and positron emission tomography (PET) scans. MRI is a medical application of nuclear magnetic resonance (NMR) which can also be used for imaging in other NMR applications, such as NMR spectroscopy. MRI is widely used in hospitals and clinics for medical diagnosis, staging and follow-up of disease. Compared to CT, MRI provides better contrast in images of soft tissues, e.g. in the brain or abdomen. However, it may be perceived as less comfortable by patients, due to the usually longer and louder measurements with the subject in a long, confining tube, although ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
