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  2. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    An example application of the Fourier transform is determining the constituent pitches in a musical waveform.This image is the result of applying a constant-Q transform (a Fourier-related transform) to the waveform of a C major piano chord.

  3. FFTW - Wikipedia

    en.wikipedia.org/wiki/FFTW

    The Fastest Fourier Transform in the West (FFTW) is a software library for computing discrete Fourier transforms (DFTs) developed by Matteo Frigo and Steven G. Johnson at the Massachusetts Institute of Technology. [2] [3] [4] FFTW is one of the fastest free software implementations of the fast Fourier transform (FFT).

  4. Multidimensional transform - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_transform

    One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation. [1] The discrete-domain multidimensional Fourier transform (FT) can be computed as follows:

  5. Gabor transform - Wikipedia

    en.wikipedia.org/wiki/Gabor_transform

    The Gabor transform, named after Dennis Gabor, is a special case of the short-time Fourier transform.It is used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time.

  6. 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.

  7. Contrast transfer function - Wikipedia

    en.wikipedia.org/wiki/Contrast_transfer_function

    Take the Fourier transform of the exit wave to obtain the wave amplitude in back focal plane of objective lens; Modify the wavefunction in reciprocal space by a phase factor, also known as the Phase Contrast Transfer Function, to account for aberrations; Inverse Fourier transform the modified wavefunction to obtain the wavefunction in the image ...

  8. Frequency domain decomposition - Wikipedia

    en.wikipedia.org/wiki/Frequency_domain_decomposition

    The frequency domain decomposition (FDD) is an output-only system identification technique popular in civil engineering, in particular in structural health monitoring.As an output-only algorithm, it is useful when the input data is unknown.

  9. DFT matrix - Wikipedia

    en.wikipedia.org/wiki/DFT_matrix

    In this case, if we make a very large matrix with complex exponentials in the rows (i.e., cosine real parts and sine imaginary parts), and increase the resolution without bound, we approach the kernel of the Fredholm integral equation of the 2nd kind, namely the Fourier operator that defines the continuous Fourier transform. A rectangular ...