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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] |
Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
White Noise
In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The term is used, with this or similar meanings, in many scientific and technical disciplines, including physics, acoustical engineering, telecommunications, and statistical forecasting. White noise refers to a statistical model for signals and signal sources, rather than to any specific signal. White noise draws its name from white light, although light that appears white generally does not have a flat power spectral density over the visible band. In discrete time, white noise is a discrete signal whose samples are regarded as a sequence of serially uncorrelated random variables with zero mean and finite variance; a single realization of white noise is a random shock. Depending on the context, one may also require that the samples be independent and have identical probability distribution (in other words independent and iden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nuttall
Nuttall may refer to: People * Nuttall (name) * Nuttall baronets Nature * Nuttall's oak, a fast-growing large deciduous oak tree native to North America * Nuttall's woodpecker, a species of woodpecker found in oak woodlands of California * Nuttall sandstone, a very hard type of sandstone; see New River Gorge National River * Nuttall's toothwort, a species of cardamine flower. Places * Nuttall, Virginia, United States * Nuttall railway station, Nuttall village, Nasirabad, Balochistan, Pakistan * Nuttalls, hills in England and Wales that are over with a prominence above Other uses * BAM Nuttall, a British construction company * Blackman–Nuttall window, a mathematical function used in signal processing—see Window function * Codex Zouche-Nuttall, a pre-Columbian piece of Mixtec writing * Geiger–Nuttall law, a rule in nuclear physics stating that short-lived isotopes emit more energetic alpha particles than long-lived ones * Nuttall Ornithological Club, the oldest ornitho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harris
Harris may refer to: Places Canada * Harris, Ontario * Northland Pyrite Mine (also known as Harris Mine) * Harris, Saskatchewan * Rural Municipality of Harris No. 316, Saskatchewan Scotland * Harris, Outer Hebrides (sometimes called the Isle of Harris), part of Lewis and Harris, Outer Hebrides * Harris, Rùm, a place on Rùm, Highland United States * Harris, Indiana * Harris, Iowa * Harris, Kansas * Harris Township, Michigan * Harris, Minnesota * Harris, Missouri * Harris, New York * Harris, North Carolina * Harris, Oregon * Harris, Wisconsin Elsewhere * Harris, Montserrat Other places with "Harris" in the name * Harrisonburg, Louisiana * Harrisonburg, Virginia * Harris County (other) * Harris Lake (other) * Harris Mountain (other) * Harris Township (other) * Harrisburg (other) * Harrison (other) * Harrisville (other) People * Harris (Essex cricketer) * Harris Jayaraj, an Indian music director * Harr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Fourier Transform
__NOTOC__ In mathematics the finite Fourier transform may refer to either *another name for discrete-time Fourier transform (DTFT) of a finite-length series. E.g., F.J.Harris (pp. 52–53) describes the ''finite Fourier transform'' as a "continuous periodic function" and the discrete Fourier transform (DFT) as "a set of samples of the finite Fourier transform". In actual implementation, that is not two separate steps; the DFT replaces the DTFT. So J.Cooley (pp. 77–78) describes the implementation as ''discrete finite Fourier transform''. or * another name for the Fourier series coefficients. or * another name for one snapshot of a 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 divi .... See also * Fourier transform Notes Refer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. As of 2020, MATLAB has more than 4 million users worldwide. They come from various backgrounds of engineering, science, and economics. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was based on his 1960s PhD thesis. Moler became a math professor at the University of New Mexico and starte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kaiser Window
The Kaiser window, also known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions used in finite impulse response filter design and spectral estimation, spectral analysis. The Kaiser window approximates the DPSS window which Spectral concentration problem, maximizes the energy concentration in the main lobe but which is difficult to compute. Definition The Kaiser window and its Fourier transform are given by: : w_0(x) \triangleq \left\ \quad \stackrel\quad \frac , where: * is the zeroth-order Modified_Bessel_function#Modified_Bessel_functions:_Iα,_Kα, modified Bessel function of the first kind, * is the window duration, and * is a non-negative real number that determines the shape of the window. In the frequency domain, it determines the trade-off between main-lobe width and side lobe level, which is a central decision in window design. * Sometimes the Kaiser window is parametrized by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectral Leakage From Two 8-point Gaussian Windows
''Spectral'' is a 2016 3D military science fiction, supernatural horror fantasy and action-adventure thriller war film directed by Nic Mathieu. Written by himself, Ian Fried, and George Nolfi from a story by Fried and Mathieu. The film stars James Badge Dale, Max Martini, Emily Mortimer, Clayne Crawford and Bruce Greenwood. The film was released worldwide on December 9, 2016 on Netflix. On February 1, 2017, Netflix released a prequel graphic novel of the film called ''Spectral: Ghosts of War'' which was made available digitally through the website ComiXology. Plot DARPA researcher Dr. Mark Clyne flies from Virginia to Moldova, the current deployment location of the US military in the ongoing Moldovan War, to be consulted on one of his creations, a line of hyperspectral imaging goggles that have been issued to troops there. After arriving at a US military airbase on the outskirts of Chișinău, he meets with US Army General Orland and CIA officer Fran Madison. They show him ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two 8-point Gaussian Window Functions
2 (two) is a number, numeral and digit. It is the natural number following 1 and preceding 3. It is the smallest and only even prime number. Because it forms the basis of a duality, it has religious and spiritual significance in many cultures. Evolution Arabic digit The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic Brahmic script, where "2" was written as two horizontal lines. The modern Chinese and Japanese languages (and Korean Hanja) still use this method. The Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic Ghubar writing, the bottom line was completely vertical, and the digit looked like a dotless closing question mark. Restoring the bottom line to its original horizonta ... [...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] |
Signal-to-noise Ratio
Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise. SNR, bandwidth, and channel capacity of a communication channel are connected by the Shannon–Hartley theorem. Definition Signal-to-noise ratio is defined as the ratio of the power of a signal (meaningful input) to the power of background noise (meaningless or unwanted input): : \mathrm = \frac, where is average power. Both signal and noise power must be measured at the same or equivalent points in a system, and within the same system bandwidth. Depending on whether the signal is a constant () or a random variable (), the signal-to-noise ratio for random noise becomes: : \mathrm = \frac where E refers to the expected value, i.e. in this case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
