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  2. Discretization - Wikipedia

    en.wikipedia.org/wiki/Discretization

    Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, discretization may also refer to modification of variable or category granularity, as when multiple discrete variables are aggregated or multiple discrete categories fused.

  3. State-space representation - Wikipedia

    en.wikipedia.org/wiki/State-space_representation

    The time variable can be continuous (e.g. ) or discrete (e.g. ). In the latter case, the time variable is usually used instead of . Hybrid systems allow for time domains that have both continuous and discrete parts. Depending on the assumptions made, the state-space model representation can assume the following forms:

  4. Discrete Fourier transform - Wikipedia

    en.wikipedia.org/wiki/Discrete_Fourier_transform

    Left: A continuous function (top) and its Fourier transform (bottom). Center-left: Periodic summation of the original function (top). Fourier transform (bottom) is zero except at discrete points. The inverse transform is a sum of sinusoids called Fourier series. Center-right: Original function is discretized (multiplied by a Dirac comb) (top).

  5. Circulant matrix - Wikipedia

    en.wikipedia.org/wiki/Circulant_matrix

    A circulant matrix is fully specified by one vector, , which appears as the first column (or row) of . The remaining columns (and rows, resp.) of C {\displaystyle C} are each cyclic permutations of the vector c {\displaystyle c} with offset equal to the column (or row, resp.) index, if lines are indexed from 0 {\displaystyle 0} to n − 1 ...

  6. Gradient discretisation method - Wikipedia

    en.wikipedia.org/wiki/Gradient_discretisation_method

    The Discontinuous Galerkin method consists in approximating problems by a piecewise polynomial function, without requirements on the jumps from an element to the other. [8] It is plugged in the GDM framework by including in the discrete gradient a jump term, acting as the regularization of the gradient in the distribution sense.

  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 distortion.

  8. 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.

  9. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    ⁠ The vector ⁠ ⁠ can be characterized as a right-singular vector corresponding to a singular value of ⁠ ⁠ that is zero. This observation means that if ⁠ A {\displaystyle \mathbf {A} } ⁠ is a square matrix and has no vanishing singular value, the equation has no non-zero ⁠ x {\displaystyle \mathbf {x} } ⁠ as a solution.