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Gaussian Window
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several ''window functions'' can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multiplying the given sampled signal by the window function. Conventions * w_0(x) is a zero-phase function (symmetrical about x=0), continuous for x \in N/2, N/2 where N is a positive integer (even or odd). * The sequence \ is ''symmetric'', of length N+1. * \ is ''DFT-symmetric'', of length N. * The parameter B displayed on each spectral plot is the function's noise equivalent bandwidth metric, in units of ''DFT bins''. The sparse sampling of a DTFT (such as the DFTs in Fig 1) only reveals the leakage into the DFT bins from a sinusoid whose frequency is als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Window Functions
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several ''window functions'' can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multiplying the given sampled signal by the window function. Conventions * w_0(x) is a zero-phase function (symmetrical about x=0), continuous for x \in N/2, N/2 where N is a positive integer (even or odd). * The sequence \ is ''symmetric'', of length N+1. * \ is ''DFT-symmetric'', of length N. * The parameter B displayed on each spectral plot is the function's noise equivalent bandwidth metric, in units of ''DFT bins''. The sparse sampling of a DTFT (such as the DFTs in Fig 1) only reveals the leakage into the DFT bins from a sinusoid whose frequency is als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Window Functions
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several ''window functions'' can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multiplying the given sampled signal by the window function. Conventions * w_0(x) is a zero-phase function (symmetrical about x=0), continuous for x \in N/2, N/2 where N is a positive integer (even or odd). * The sequence \ is ''symmetric'', of length N+1. * \ is ''DFT-symmetric'', of length N. * The parameter B displayed on each spectral plot is the function's noise equivalent bandwidth metric, in units of ''DFT bins''. The sparse sampling of a DTFT (such as the DFTs in Fig 1) only reveals the leakage into the DFT bins from a sinusoid whose frequency is als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, normally symmetric around the middle of the interval, usually near a maximum in the middle, and usually tapering 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 determined in ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boxcar Window
In discrete-time signal processing, windowing is a preliminary signal shaping technique, usually applied to improve the appearance and usefulness of a subsequent Discrete Fourier Transform. Several ''window functions'' can be defined, based on a constant (rectangular window), B-splines, other polynomials, sinusoids, cosine-sums, adjustable, hybrid, and other types. The windowing operation consists of multiplying the given sampled signal by the window function. Conventions * w_0(x) is a zero-phase function (symmetrical about x=0), continuous for x \in N/2, N/2 where N is a positive integer (even or odd). * The sequence \ is ''symmetric'', of length N+1. * \ is ''DFT-symmetric'', of length N. * The parameter B displayed on each spectral plot is the function's noise equivalent bandwidth metric, in units of ''DFT bins''. The sparse sampling of a DTFT (such as the DFTs in Fig 1) only reveals the leakage into the DFT bins from a sinusoid whose frequency is als ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Window Function And Frequency Response - Cosine
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] |
Autocorrelation
Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay. Informally, it is the similarity between observations of a random variable as a function of the time lag between them. The analysis of autocorrelation is a mathematical tool for finding repeating patterns, such as the presence of a periodic signal obscured by noise, or identifying the missing fundamental frequency in a signal implied by its harmonic frequencies. It is often used in signal processing for analyzing functions or series of values, such as time domain signals. Different fields of study define autocorrelation differently, and not all of these definitions are equivalent. In some fields, the term is used interchangeably with autocovariance. Unit root processes, trend-stationary processes, autoregressive processes, and moving average processes are specific forms of processes with autocorrelation. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Window Function And Its Fourier Transform – Hann (n = 0
A window is an Hole, 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 glazing (window), glazed or covered in some other transparency (optics), transparent or translucent material, a Window sash, 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 (architecture), ventilation, or closed, to exclude inclement weather. Windows may have a Latch (hardware), latch or similar Mechanism (engineering), mechanism to Lock and key, lock the window shut or to hold it open by various amounts. In addition to this, many Modernity, modern day windows may have a window screen or mesh, often made of Aluminium, aluminum or Fiberglass, fibreglass, to keep Bug (insect), bugs out when the window is opened. Types include the eyebrow window, fixed windows, hexagonal windows, single-hung, and double-hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Window Function And Frequency Response - Hamming (alpha = 0
A window is an Hole, 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 glazing (window), glazed or covered in some other transparency (optics), transparent or translucent material, a Window sash, 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 (architecture), ventilation, or closed, to exclude inclement weather. Windows may have a Latch (hardware), latch or similar Mechanism (engineering), mechanism to Lock and key, lock the window shut or to hold it open by various amounts. In addition to this, many Modernity, modern day windows may have a window screen or mesh, often made of Aluminium, aluminum or Fiberglass, fibreglass, to keep Bug (insect), bugs out when the window is opened. Types include the eyebrow window, fixed windows, hexagonal windows, single-hung, and double-hu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julius Von Hann
Julius Ferdinand von Hann (23 March 1839 in Wartberg ob der Aist near Linz – 1 October 1921 in Vienna) was an Austrian meteorologist. He is seen as a father of modern meteorology. Biography He was educated at the gymnasium of Kremsmünster and then studied mathematics, chemistry and physics at the University of Vienna, then geology and paleontology under Eduard Suess and physical geography under Friedrich Simony. From 1865 to 1868, he was master at the ''Oberrealschule'' at Linz, and in 1865 was invited by Karl Jelinek to become the first editor of the '' Zeitschrift für Meteorologie''. In 1877, he succeeded Jelinek as the director of the Meteorologische Zentralanstalt (Central Institute for Meteorology and Earth Magnetism) and was appointed professor of meteorology at the University of Vienna. In 1897, he retired as director and became professor of meteorology at the University of Graz, but returned to Vienna to fill the chair of professor of cosmic physics in 1900, where h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard W
Richard is a male given name. It originates, via Old French, from Old Frankish and is a compound of the words descending from Proto-Germanic ''*rīk-'' 'ruler, leader, king' and ''*hardu-'' 'strong, brave, hardy', and it therefore means 'strong in rule'. Nicknames include "Richie", "Dick", "Dickon", " Dickie", "Rich", "Rick", "Rico", "Ricky", and more. Richard is a common English, German and French male name. It's also used in many more languages, particularly Germanic, such as Norwegian, Danish, Swedish, Icelandic, and Dutch, as well as other languages including Irish, Scottish, Welsh and Finnish. Richard is cognate with variants of the name in other European languages, such as the Swedish "Rickard", the Catalan "Ricard" and the Italian "Riccardo", among others (see comprehensive variant list below). People named Richard Multiple people with the same name * Richard Andersen (other) * Richard Anderson (other) * Richard Cartwright (other) * Ri ... [...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 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) 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, for instance, produces leakage, which we call ''aliases'' of the original spectral component. For Fourier transform purposes, 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 product of s(t) with a different kind of function, the window function. Window functions happen to have fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parabola
In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point (the focus) and a line (the directrix). The focus does not lie on the directrix. The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
