Non-uniform discrete Fourier transformIn applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.
Fractional Fourier transformIn mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.
Haar waveletIn mathematics, the Haar wavelet is a sequence of rescaled "square-shaped" functions which together form a wavelet family or basis. Wavelet analysis is similar to Fourier analysis in that it allows a target function over an interval to be represented in terms of an orthonormal basis. The Haar sequence is now recognised as the first known wavelet basis and is extensively used as a teaching example. The Haar sequence was proposed in 1909 by Alfréd Haar.
Gabor waveletGabor wavelets are wavelets invented by Dennis Gabor using complex functions constructed to serve as a basis for Fourier transforms in information theory applications. They are very similar to Morlet wavelets. They are also closely related to Gabor filters. The important property of the wavelet is that it minimizes the product of its standard deviations in the time and frequency domain. Put another way, the uncertainty in information carried by this wavelet is minimized.
Absorption spectroscopyAbsorption spectroscopy refers to spectroscopic techniques that measure the absorption of electromagnetic radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a function of frequency, and this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum.
Static light scatteringStatic light scattering is a technique in physical chemistry that measures the intensity of the scattered light to obtain the average molecular weight Mw of a macromolecule like a polymer or a protein in solution. Measurement of the scattering intensity at many angles allows calculation of the root mean square radius, also called the radius of gyration Rg. By measuring the scattering intensity for many samples of various concentrations, the second virial coefficient, A2, can be calculated.
Dynamic light scatteringDynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution. In the scope of DLS, temporal fluctuations are usually analyzed using the intensity or photon auto-correlation function (also known as photon correlation spectroscopy - PCS or quasi-elastic light scattering - QELS). In the time domain analysis, the autocorrelation function (ACF) usually decays starting from zero delay time, and faster dynamics due to smaller particles lead to faster decorrelation of scattered intensity trace.
X-ray spectroscopyX-ray spectroscopy is a general term for several spectroscopic techniques for characterization of materials by using x-ray radiation. When an electron from the inner shell of an atom is excited by the energy of a photon, it moves to a higher energy level. When it returns to the low energy level, the energy which it previously gained by the excitation is emitted as a photon which has a wavelength that is characteristic for the element (there could be several characteristic wavelengths per element).
Sine and cosine transformsIn mathematics, the Fourier sine and cosine transforms are forms of the Fourier transform that do not use complex numbers or require negative frequency. They are the forms originally used by Joseph Fourier and are still preferred in some applications, such as signal processing or statistics. The Fourier sine transform of f(t), sometimes denoted by either or , is If t means time, then ξ is frequency in cycles per unit time, but in the abstract, they can be any pair of variables which are dual to each other.
Compton scatteringCompton scattering (also called the Compton effect) discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. It results in a decrease in energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), called the Compton effect. Part of the energy of the photon is transferred to the recoiling particle.
