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Lanczos Window
filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample of the given signal to a translated and scaled copy of the Lanczos kernel, which is a sinc function windowed by the central lobe of a second, longer, sinc function. The sum of these translated and scaled kernels is then evaluated at the desired points. Lanczos resampling is typically used to increase the sampling rate of a digital signal, or to shift it by a fraction of the sampling interval. It is often used also for multivariate interpolation, for example to resize or rotate a digital image. It has been considered the "best compromise" among several simple filters for this purpose. The filter is named after its inventor, Cornelius Lanczos (). Definition Lanczos kernel The effect of each input sample on the interpolated values i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-pass Filter
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter design. The filter is sometimes called a high-cut filter, or treble-cut filter in audio applications. A low-pass filter is the complement of a high-pass filter. In optics, high-pass and low-pass may have different meanings, depending on whether referring to frequency or wavelength of light, since these variables are inversely related. High-pass frequency filters would act as low-pass wavelength filters, and vice versa. For this reason it is a good practice to refer to wavelength filters as ''short-pass'' and ''long-pass'' to avoid confusion, which would correspond to ''high-pass'' and ''low-pass'' frequencies. Low-pass filters exist in many different forms, including electronic circuits such as a hiss filter used in audio, anti-aliasing fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Floor Function
In mathematics and computer science, the floor function is the function that takes as input a real number , and gives as output the greatest integer less than or equal to , denoted or . Similarly, the ceiling function maps to the least integer greater than or equal to , denoted or . For example, , , , and . Historically, the floor of has been–and still is–called the integral part or integer part of , often denoted (as well as a variety of other notations). Some authors may define the integral part as if is nonnegative, and otherwise: for example, and . The operation of truncation generalizes this to a specified number of digits: truncation to zero significant digits is the same as the integer part. For an integer, . Notation The ''integral part'' or ''integer part'' of a number ( in the original) was first defined in 1798 by Adrien-Marie Legendre in his proof of the Legendre's formula. Carl Friedrich Gauss introduced the square bracket notation in hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Steven Gabriel
Stephen or Steven is a common English first name. It is particularly significant to Christians, as it belonged to Saint Stephen ( grc-gre, Στέφανος ), an early disciple and deacon who, according to the Book of Acts, was stoned to death; he is widely regarded as the first martyr (or "protomartyr") of the Christian Church. In English, Stephen is most commonly pronounced as ' (). The name, in both the forms Stephen and Steven, is often shortened to Steve or Stevie. The spelling as Stephen can also be pronounced which is from the Greek original version, Stephanos. In English, the female version of the name is Stephanie. Many surnames are derived from the first name, including Stephens, Stevens, Stephenson, and Stevenson, all of which mean "Stephen's (son)". In modern times the name has sometimes been given with intentionally non-standard spelling, such as Stevan or Stevon. A common variant of the name used in English is Stephan ; related names that have found some curr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kenneth Turkowski
Kenneth is an English given name and surname. The name is an Anglicised form of two entirely different Gaelic personal names: ''Cainnech'' and '' Cináed''. The modern Gaelic form of ''Cainnech'' is ''Coinneach''; the name was derived from a byname meaning "handsome", "comely". A short form of ''Kenneth'' is '' Ken''. Etymology The second part of the name ''Cinaed'' is derived either from the Celtic ''*aidhu'', meaning "fire", or else Brittonic ''jʉ:ð'' meaning "lord". People :''(see also Ken (name) and Kenny)'' Places In the United States: * Kenneth, Indiana * Kenneth, Minnesota * Kenneth City, Florida In Scotland: * Inch Kenneth, an island off the west coast of the Isle of Mull Other * "What's the Frequency, Kenneth?", a song by R.E.M. * Hurricane Kenneth * Cyclone Kenneth Intense Tropical Cyclone Kenneth was the strongest tropical cyclone to make landfall in Mozambique since modern records began. The cyclone also caused significant damage in the Comoro Islands and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal. Aliasing can occur in signals sampled in time, for instance digital audio, or the stroboscopic effect, and is referred to as temporal aliasing. It can also occur in spatially sampled signals (e.g. moiré patterns in digital images); this type of aliasing is called spatial aliasing. Aliasing is generally avoided by applying low-pass filters or anti-aliasing filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering should then be used when restoring the sampled signal to the continuous domain or converting a signal from a lower to a higher sampling rate. For spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the function domain containing the elements which are not mapped to zero. If the domain of f is a topological space, then the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis. Formulation Suppose that f : X \to \R is a real-valued function whose domain is an arbitrary set X. The of f, written \operatorname(f), is the set of points in X where f is non-zero: \operatorname(f) = \. The support of f is the smallest subset of X with the property that f is zero on the subset's complement. If f(x) = 0 for all but a finite number of points x \in X, then f is said to have . If the set X has an additional structure (for example, a topology), then the support of f is defined in an analogous way as the smallest subset of X of an appropriate type such that f vanishes in an appropriate sense on its complement. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Filter
In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given cutoff frequency, without affecting lower frequencies, and has linear phase response. The filter's impulse response is a sinc function in the time domain and its frequency response is a rectangular function. It is an "ideal" low-pass filter in the frequency sense, perfectly passing low frequencies, perfectly cutting high frequencies; and thus may be considered to be a ''brick-wall filter''. Real-time filters can only approximate this ideal, since an ideal sinc filter (a.k.a. ''rectangular filter'') is non-causal and has an infinite delay, but it is commonly found in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula. In mathematical terms, the desired frequency response is the rectangular function: :H(f) = \operatorname \left( \frac \right) = \begin 0, & \text , f, > B, \\ \frac, & \text , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandlimiting
Bandlimiting is the limiting of a signal's frequency domain representation or spectral density to zero above a certain finite frequency. A band-limited signal is one whose Fourier transform or spectral density has bounded support. A bandlimited signal may be either random (stochastic) or non-random (deterministic). In general, infinitely many terms are required in a continuous Fourier series representation of a signal, but if a finite number of Fourier series terms can be calculated from that signal, that signal is considered to be band-limited. Sampling bandlimited signals A bandlimited signal can be fully reconstructed from its samples, provided that the sampling rate exceeds twice the maximum frequency in the bandlimited signal. This minimum sampling rate is called the Nyquist rate. This result, usually attributed to Nyquist and Shannon, is known as the Nyquist–Shannon sampling theorem. An example of a simple deterministic bandlimited signal is a sinusoid of the for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Window Function And Frequency Response - Lanczos
A window is an opening in a wall, door, roof, or vehicle that allows the exchange of light and may also allow the passage of sound and sometimes air. Modern windows are usually glazed or covered in some other transparent or translucent material, a sash set in a frame in the opening; the sash and frame are also referred to as a window. Many glazed windows may be opened, to allow ventilation, or closed, to exclude inclement weather. Windows may have a latch or similar mechanism to lock the window shut or to hold it open by various amounts. In addition to this, many modern day windows may have a window screen or mesh, often made of aluminum or fibreglass, to keep bugs out when the window is opened. Types include the eyebrow window, fixed windows, hexagonal windows, single-hung, and double-hung sash windows, horizontal sliding sash windows, casement windows, awning windows, hopper windows, tilt, and slide windows (often door-sized), tilt and turn windows, transom windows, sidel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Interpolation - Sheet Music, Interpolated
__NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians. Biography He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from the Middle Ages into the 20th century. The Principality of Hungary emerged as a Christian kingdom upon the coronation of the first king Stephen ... to Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lanczos Interpolation - Sheet Music, Original
__NOTOC__ Cornelius (Cornel) Lanczos ( hu, Lánczos Kornél, ; born as Kornél Lőwy, until 1906: ''Löwy (Lőwy) Kornél''; February 2, 1893 – June 25, 1974) was a Hungarian-American and later Hungarian-Irish mathematician and physicist. According to György Marx he was one of The Martians. Biography He was born in Fehérvár (Alba Regia), Fejér County, Kingdom of Hungary to Károly Lőwy and Adél Hahn. Lanczos' Ph.D. thesis (1921) was on relativity theory. He sent his thesis copy to Albert Einstein, and Einstein wrote back, saying: "I studied your paper as far as my present overload allowed. I believe I may say this much: this does involve competent and original brainwork, on the basis of which a doctorate should be obtainable ... I gladly accept the honorable dedication."Barbara Gellai (2010) ''The Intrinsic Nature of Things: the life and science of Cornelius Lanczos'', American Mathematical Society In 1924 he discovered an exact solution of the Einstein field equatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Series
A Fourier series () is a summation of harmonically related sinusoidal functions, also known as components or harmonics. The result of the summation is a periodic function whose functional form is determined by the choices of cycle length (or ''period''), the number of components, and their amplitudes and phase parameters. With appropriate choices, one cycle (or ''period'') of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). The number of components is theoretically infinite, in which case the other parameters can be chosen to cause the series to converge to almost any ''well behaved'' periodic function (see Pathological and Dirichlet–Jordan test). The components of a particular function are determined by ''analysis'' techniques described in this article. Sometimes the components are known first, and the unknown function is ''synthesized'' by a Fourier series. Such is the case of a discrete-ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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