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  2. 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.

  3. 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 ...

  4. 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

  5. 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.

  6. Multitaper - Wikipedia

    en.wikipedia.org/wiki/Multitaper

    The multitaper method overcomes some of the limitations of non-parametric Fourier analysis. When applying the Fourier transform to extract spectral information from a signal, we assume that each Fourier coefficient is a reliable representation of the amplitude and relative phase of the corresponding component frequency. This assumption, however ...

  7. Multidimensional transform - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_transform

    The conversion from continuous time to samples (discrete-time) changes the underlying Fourier transform of x(t) into a discrete-time Fourier transform (DTFT), which generally entails a type of distortion called aliasing. Choice of an appropriate sample-rate (see Nyquist rate) is the key to minimizing that

  8. List of Fourier transforms - Wikipedia

    en.wikipedia.org/?title=List_of_Fourier...

    This page was last edited on 21 September 2011, at 17:03 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  9. 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.