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  2. Multidimensional transform - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_transform

    The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex frequency domain in which the 2D surface in 4D space that the Fourier transform lies on is known as the unit surface or unit bicircle.

  3. Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Fourier_transform

    [note 2] The Fourier transform can also be generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional 'position space' to a function of 3-dimensional momentum (or a function of space and time to a function of 4-momentum).

  4. 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 ...

  5. Discrete Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Fourier_transform

    Fig 2: Depiction of a Fourier transform (upper left) and its periodic summation (DTFT) in the lower left corner. The spectral sequences at (a) upper right and (b) lower right are respectively computed from (a) one cycle of the periodic summation of s(t) and (b) one cycle of the periodic summation of the s(nT) sequence.

  6. 2D Z-transform - Wikipedia

    en.wikipedia.org/wiki/2D_Z-transform

    The 2D Z-transform, similar to the Z-transform, is used in multidimensional signal processing to relate a two-dimensional discrete-time signal to the complex frequency domain in which the 2D surface in 4D space that the Fourier transform lies on is known as the unit surface or unit bicircle. [1] The 2D Z-transform is defined by

  7. Projection-slice theorem - Wikipedia

    en.wikipedia.org/wiki/Projection-slice_theorem

    Take that same function, but do a two-dimensional Fourier transform first, and then slice it through its origin, which is parallel to the projection line. In operator terms, if F 1 and F 2 are the 1- and 2-dimensional Fourier transform operators mentioned above, P 1 is the projection operator (which projects a 2-D function onto a 1-D line),

  8. Two-dimensional infrared spectroscopy - Wikipedia

    en.wikipedia.org/wiki/Two-dimensional_infrared...

    The Fourier transform with respect to provides the excitation spectrum (frequency ). Two-dimensional infrared spectroscopy (2D IR) is a nonlinear infrared spectroscopy technique that has the ability to correlate vibrational modes in condensed-phase systems. This technique provides information beyond linear infrared spectra, by spreading the ...

  9. Two-dimensional window design - Wikipedia

    en.wikipedia.org/wiki/Two-dimensional_window_design

    The transformation of the Fourier transform of the window function in rectangular co-ordinates to polar co-ordinates results in a Fourier–Bessel transform expression which is called as Hankel transform. Hence the Hankel transform is used to compute the Fourier transform of the 2-D window functions.

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