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  2. Gabor wavelet - Wikipedia

    en.wikipedia.org/wiki/Gabor_wavelet

    The equation of a 1-D Gabor wavelet is a Gaussian modulated by a complex exponential, described as follows: [3] = / ()As opposed to other functions commonly used as bases in Fourier Transforms such as and , Gabor wavelets have the property that they are localized, meaning that as the distance from the center increases, the value of the function becomes exponentially suppressed.

  3. List of Fourier-related transforms - Wikipedia

    en.wikipedia.org/wiki/List_of_Fourier-related...

    These are called Fourier series coefficients. The term Fourier series actually refers to the inverse Fourier transform, which is a sum of sinusoids at discrete frequencies, weighted by the Fourier series coefficients. When the non-zero portion of the input function has finite duration, the Fourier transform is continuous and finite-valued.

  4. Gerchberg–Saxton algorithm - Wikipedia

    en.wikipedia.org/wiki/Gerchberg–Saxton_algorithm

    The original paper by Gerchberg and Saxton considered image and diffraction pattern of a sample acquired in an electron microscope. It is often necessary to know only the phase distribution from one of the planes, since the phase distribution on the other plane can be obtained by performing a Fourier transform on the plane whose phase is known.

  5. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    The trade-off between the compaction of a function and its Fourier transform can be formalized in the form of an uncertainty principle by viewing a function and its Fourier transform as conjugate variables with respect to the symplectic form on the time–frequency domain: from the point of view of the linear canonical transformation, the ...

  6. List of Fourier analysis topics - Wikipedia

    en.wikipedia.org/wiki/List_of_Fourier_analysis...

    List of Fourier-related transforms; Fourier transform on finite groups; Fractional Fourier transform; Continuous Fourier transform; Fourier operator; Fourier inversion theorem; Sine and cosine transforms; Parseval's theorem; Paley–Wiener theorem; Projection-slice theorem; Frequency spectrum

  7. Spectral method - Wikipedia

    en.wikipedia.org/wiki/Spectral_method

    Compute the Fourier transform (b j,k) of g.Compute the Fourier transform (a j,k) of f via the formula ().Compute f by taking an inverse Fourier transform of (a j,k).; Since we're only interested in a finite window of frequencies (of size n, say) this can be done using a fast Fourier transform algorithm.

  8. Floor and ceiling functions - Wikipedia

    en.wikipedia.org/wiki/Floor_and_ceiling_functions

    The fractional part function has Fourier series expansion [19] {} = = ⁡ for x not an integer. At points of discontinuity, a Fourier series converges to a value that is the average of its limits on the left and the right, unlike the floor, ceiling and fractional part functions: for y fixed and x a multiple of y the Fourier series given ...

  9. Spectral leakage - Wikipedia

    en.wikipedia.org/wiki/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 of the non-zero values of S(f).