|
Window Function
In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval. Typically, window functions are symmetric around the middle of the interval, approach a maximum in the middle, and taper away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window". Equivalently, and in actual practice, the segment of data within the window is first isolated, and then only that data is multiplied by the window function values. Thus, tapering, not segmentation, is the main purpose of window functions. The reasons for examining segments of a longer function include detection of transient events and time-averaging of frequency spectra. The duration of the segments is determine ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hanning
Hanning is a surname. Notable people with the surname include: *Loy Hanning (1917–1986), American Major League Baseball pitcher *Reinhold Hanning (1921–2017), German SS guard at Auschwitz concentration camp *Rob Hanning, American television writer and producer *Robert W. Hanning, American medievalist See also *Hann function, a discrete window function *John Hanning Speke (1827–1864), English explorer and officer {{Surname, Hanning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighting
The process of frequency weighting involves emphasizing the contribution of particular aspects of a phenomenon (or of a set of data) over others to an outcome or result; thereby highlighting those aspects in comparison to others in the analysis. That is, rather than each variable in the data set contributing equally to the final result, some of the data is adjusted to make a greater contribution than others. This is analogous to the practice of adding (extra) weight to one side of a pair of scales in order to favour either the buyer or seller. While weighting may be applied to a set of data, such as epidemiological data, it is more commonly applied to measurements of light, heat, sound, gamma radiation, and in fact any stimulus that is spread over a spectrum of frequencies. Weighting in acoustics Weighting and loudness In the measurement of loudness, for example, a weighting filter is commonly used to emphasise frequencies around 3 to 6 kHz where the human ear is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Leakage
The Fourier transform of a function of time, s(t), is a complex-valued function of frequency, S(f), often referred to as a frequency spectrum. Any LTI system theory, linear time-invariant operation on s(t) produces a new spectrum of the form H(f)•S(f), which changes the relative magnitudes and/or angles (Phase (waves), phase) of the non-zero values of S(f). Any other type of operation creates new frequency components that may be referred to as spectral leakage in the broadest sense. Sampling (signal processing), Sampling, for instance, produces leakage, which we call ''aliasing, aliases'' of the original spectral component. For Fourier transform purposes, Sampling (signal processing), sampling is modeled as a product between s(t) and a Dirac comb function. The spectrum of a product is the convolution between S(f) and another function, which inevitably creates the new frequency components. But the term 'leakage' usually refers to the effect of ''windowing'', which is the produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Airy Function
In the physical sciences, the Airy function (or Airy function of the first kind) is a special function named after the British astronomer George Biddell Airy (1801–1892). The function Ai(''x'') and the related function Bi(''x''), are Linear independence, linearly independent solutions to the differential equation \frac - xy = 0 , known as the Airy equation or the Stokes equation. Because the solution of the linear differential equation \frac - ky = 0 is oscillatory for and exponential for , the Airy functions are oscillatory for and exponential for . In fact, the Airy equation is the simplest second-order linear differential equation with a turning point (a point where the character of the solutions changes from oscillatory to exponential). Definitions For real values of , the Airy function of the first kind can be defined by the improper integral, improper Riemann integral: \operatorname(x) = \dfrac\int_0^\infty\cos\left(\dfrac + xt\right)\, dt\equiv \dfrac \lim_ \in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diffraction
Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the Wave propagation, propagating wave. Diffraction is the same physical effect as Wave interference, interference, but interference is typically applied to superposition of a few waves and the term diffraction is used when many waves are superposed. Italian scientist Francesco Maria Grimaldi coined the word ''diffraction'' and was the first to record accurate observations of the phenomenon in 1660 in science, 1660. In classical physics, the diffraction phenomenon is described by the Huygens–Fresnel principle that treats each point in a propagating wavefront as a collection of individual spherical wavelets. The characteristic pattern is most pronounced when a wave from a Coherence (physics), coherent source (such as a laser) encounters a slit/aperture tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anisotropy
Anisotropy () is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength. An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions). Fields of interest Computer graphics In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet. Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and viewed at a shallow angle. Older ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Window
In signal processing and statistics, a window function (also known as an apodization function or tapering function) is a function (mathematics), mathematical function that is zero-valued outside of some chosen interval (mathematics), interval. Typically, window functions are symmetric around the middle of the interval, approach a maximum in the middle, and taper away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window". Equivalently, and in actual practice, the segment of data within the window is first isolated, and then only that data is multiplied by the window function values. Thus, tapering, not segmentation, is the main purpose of window functions. The reasons for examining segments of a longer function include detection of transient events and time-averaging of frequency spec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotropy
In physics and geometry, isotropy () is uniformity in all orientations. Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radial Function
In mathematics, a radial function is a real-valued function defined on a Euclidean space whose value at each point depends only on the distance between that point and the origin. The distance is usually the Euclidean distance. For example, a radial function in two dimensions has the form \Phi(x,y) = \varphi(r), \quad r = \sqrt where is a function of a single non-negative real variable. Radial functions are contrasted with spherical functions, and any descent function (e.g., continuous and rapidly decreasing) on Euclidean space can be decomposed into a series consisting of radial and spherical parts: the solid spherical harmonic expansion. A function is radial if and only if it is invariant under all rotations leaving the origin fixed. That is, is radial if and only if f\circ \rho = f\, for all , the special orthogonal group in dimensions. This characterization of radial functions makes it possible also to define radial distributions. These are distributions on su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modified Discrete Cosine Transform
The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where subsequent blocks are overlapped so that the last half of one block coincides with the first half of the next block. This overlapping, in addition to the energy-compaction qualities of the DCT, makes the MDCT especially attractive for signal compression applications, since it helps to avoid artifacts stemming from the block boundaries. As a result of these advantages, the MDCT is the most widely used lossy compression technique in audio data compression. It is employed in most modern audio coding standards, including MP3, Dolby Digital (AC-3), Vorbis (Ogg), Windows Media Audio (WMA), ATRAC, Cook, Advanced Audio Coding (AAC), High-Definition Coding (HDC), LDAC, Dolby AC-4, and MPEG-H 3D Audio, as well as speech coding standards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Welch Method
Welch's method, named after Peter D. Welch, is an approach for spectral density estimation. It is used in physics, engineering, and applied mathematics for estimating the power of a signal at different frequencies. The method is based on the concept of using periodogram spectrum estimates, which are the result of converting a signal from the time domain to the frequency domain. Welch's method is an improvement on the standard periodogram spectrum estimating method and on Bartlett's method, in that it reduces noise in the estimated power spectra in exchange for reducing the frequency resolution. Due to the noise caused by imperfect and finite data, the noise reduction from Welch's method is often desired. Definition and procedure The Welch method is based on Bartlett's method and differs in two ways: # The signal is split up into overlapping segments: the original data segment is split up into L data segments of length M, overlapping by D points. ## If D = M / 2, the overla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Fourier Transform
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced Sampling (signal processing), samples of a function (mathematics), function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex number, complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence. An inverse DFT (IDFT) is a Fourier series, using the DTFT samples as coefficients of complex number, complex Sine wave, sinusoids at the corresponding DTFT frequencies. It has the same sample-values as the original input sequence. The DFT is therefore said to be a frequency domain representation of the original input sequence. If the original sequence spans all the non-zero values of a function, its DTFT is continuous (and periodic), and the DFT provides discrete samples of one cycle. If the original sequence is one cycle of a periodic fu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
