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  2. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    In other words, where f is a (normalized) Gaussian function with variance σ 2 /2 π, centered at zero, and its Fourier transform is a Gaussian function with variance σ −2 /2 π. Gaussian functions are examples of Schwartz functions (see the discussion on tempered distributions below).

  3. Fourier number - Wikipedia

    en.wikipedia.org/wiki/Fourier_number

    In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, . This dimensionless group is named in honor of J.B.J. Fourier , who formulated the modern understanding of heat conduction. [ 1 ]

  4. Multidimensional transform - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_transform

    where "FFT" denotes the fast Fourier transform, and f is the spatial frequency spans from 0 to N/2 – 1. The proposed FFT-based imaging approach is diagnostic technology to ensure a long life and stable to culture arts. This is a simple, cheap which can be used in museums without affecting their daily use.

  5. Fourier analysis - Wikipedia

    en.wikipedia.org/wiki/Fourier_analysis

    Lectures on Image Processing: A collection of 18 lectures in pdf format from Vanderbilt University. Lecture 6 is on the 1- and 2-D Fourier Transform. Lectures 7–15 make use of it., by Alan Peters; Moriarty, Philip; Bowley, Roger (2009). "Σ Summation (and Fourier Analysis)". Sixty Symbols. Brady Haran for the University of Nottingham.

  6. Structure factor - Wikipedia

    en.wikipedia.org/wiki/Structure_factor

    An alternative derivation gives good insight, but uses Fourier transforms and convolution. To be general, consider a scalar (real) quantity ϕ ( r ) {\displaystyle \phi (\mathbf {r} )} defined in a volume V {\displaystyle V} ; this may correspond, for instance, to a mass or charge distribution or to the refractive index of an inhomogeneous medium.

  7. Short-time Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Short-time_Fourier_transform

    Taking the Fourier transform produces N complex coefficients. Of these coefficients only half are useful (the last N/2 being the complex conjugate of the first N/2 in reverse order, as this is a real valued signal). These N/2 coefficients represent the frequencies 0 to f s /2 (Nyquist) and two consecutive coefficients are spaced apart by f s /N Hz.

  8. Fourier series - Wikipedia

    en.wikipedia.org/wiki/Fourier_series

    A Fourier series (/ ˈ f ʊr i eɪ,-i ər / [1]) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. [2] By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are ...

  9. Fourier - Wikipedia

    en.wikipedia.org/wiki/Fourier

    Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function; Fourier analysis, the description of functions as sums of sinusoids; Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series