Definition, Meaning & Synonyms | English word CONVOLUTION

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Definitions of CONVOLUTION

1. A twist or fold.
2. Any of the folds on the surface of the brain.
3. The shape of something rotating; a vortex.
4. The state or condition of being convoluted.
5. One 360° turn in a spring or similar helix.
6. (mathematics, functional analysis) A mathematical operation on two functions that produces a third that expresses how the shape of one is modified by the other; the integral of the product of the two functions after one is reflected about the y-axis and shifted along the x-axis.
7. (computing) A function which maps a tuple of sequences into a sequence of tuples.

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Examples of Using CONVOLUTION in a Sentence

• This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic polynomial equations, and by simplifying convolution into multiplication.
• ε(n): the function defined by ε(n) = 1 if n = 1 and 0 otherwise, sometimes called multiplication unit for Dirichlet convolution or simply the unit function (completely multiplicative).
• In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms.
• On this underlying set one defines addition and scalar multiplication pointwise, and "multiplication" in the incidence algebra is a convolution defined by.
• In mathematics, the Dirichlet convolution (or divisor convolution) is a binary operation defined for arithmetic functions; it is important in number theory.
• Rader of MIT Lincoln Laboratory, is a fast Fourier transform (FFT) algorithm that computes the discrete Fourier transform (DFT) of prime sizes by re-expressing the DFT as a cyclic convolution (the other algorithm for FFTs of prime sizes, Bluestein's algorithm, also works by rewriting the DFT as a convolution).
• The use of zero-padding for the convolution in Bluestein's algorithm deserves some additional comment.
• Related is the Gibbs phenomenon: If the sine integral is considered as the convolution of the sinc function with the heaviside step function, this corresponds to truncating the Fourier series, which is the cause of the Gibbs phenomenon.
• The effect of filtering can be modeled as a convolution between a trapezoidal function that describes the illumination and one or more bandpass filters.
• The frequency response allows simpler analysis of cascaded systems such as multistage amplifiers, as the response of the overall system can be found through multiplication of the individual stages' frequency responses (as opposed to convolution of the impulse response in the time domain).
• Mollifiers are an important special case of bump functions as they can be used in distribution theory to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution.
• The Mellin transform may also be viewed as the Gelfand transform for the convolution algebra of the locally compact abelian group of positive real numbers with multiplication.
• This and many of the following series may be obtained by applying Möbius inversion and Dirichlet convolution to known series.
• The turbo principle is generalized now by Claude Berrou and his lab team for the processing of various functions such as the demodulation, the detection or the equalization using a network of multiple convolution codes working in parallel with probabilistic feedback.
• In spectroscopy, a Voigt profile results from the convolution of two broadening mechanisms, one of which alone would produce a Gaussian profile (usually, as a result of the Doppler broadening), and the other would produce a Lorentzian profile.
• Although no commercially successful general-purpose computer hardware has used a dataflow architecture, it has been successfully implemented in specialized hardware such as in digital signal processing, network routing, graphics processing, telemetry, and more recently in data warehousing, and artificial intelligence (as: polymorphic dataflow Convolution Engine, structure-driven, dataflow scheduling).
• The first approach is "XF" correlation because it first cross-correlates antennas (the "X" operation) using a time-domain "lag" convolution, and then computes the spectrum (the "F" operation) for each resulting baseline.
• By using FFT (fast Fourier transform), used in the original version rather than NTT (Number-theoretic transform), with convolution rule; we get.
• Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm.
• com/books?id=JHFrHfxzJ_IC Convolution and equidistribution: Sato-Tate theorems for finite-field Mellin transforms.

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