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  2. Multidimensional discrete convolution - Wikipedia

    en.wikipedia.org/wiki/Multidimensional_discrete...

    In signal processing, multidimensional discrete convolution refers to the mathematical operation between two functions f and g on an n-dimensional lattice that produces a third function, also of n-dimensions. Multidimensional discrete convolution is the discrete analog of the multidimensional convolution of functions on Euclidean space.

  3. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    A discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing. [citation needed]

  4. Fast Algorithms for Multidimensional Signals - Wikipedia

    en.wikipedia.org/wiki/Fast_Algorithms_for...

    A multidimensional (M-D) signal can be modeled as a function of M independent variables, where M is greater than or equal to 2. These signals may be categorized as continuous, discrete, or mixed. A continuous signal can be modeled as a function of independent variables which range over a continuum of values, example – an audio wave travelling ...

  5. 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.

  6. Parallel multidimensional digital signal processing - Wikipedia

    en.wikipedia.org/wiki/Parallel_Multidimensional...

    The following derivation is a close paraphrasing from the classical text Multidimensional Digital Signal Processing. [22] The row-column decomposition can be applied to an arbitrary number of dimensions, but for illustrative purposes, the 2D row-column decomposition of the DFT will be described first. The 2D DFT is defined as

  7. Convolution theorem - Wikipedia

    en.wikipedia.org/wiki/Convolution_theorem

    In mathematics, the convolution theorem states that under suitable conditions the Fourier transform of a convolution of two functions (or signals) is the product of their Fourier transforms. More generally, convolution in one domain (e.g., time domain) equals point-wise multiplication in the other domain (e.g., frequency domain).

  8. Overlap–add method - Wikipedia

    en.wikipedia.org/wiki/Overlap–add_method

    DFT N and IDFT N refer to the Discrete Fourier transform and its inverse, evaluated over discrete points, and L {\displaystyle L} is customarily chosen such that N = L + M − 1 {\displaystyle N=L+M-1} is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.

  9. Kernel (image processing) - Wikipedia

    en.wikipedia.org/wiki/Kernel_(image_processing)

    2D Convolution Animation. Convolution is the process of adding each element of the image to its local neighbors, weighted by the kernel. This is related to a form of mathematical convolution. The matrix operation being performed—convolution—is not traditional matrix multiplication, despite being similarly denoted by *.