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  2. Convolution - Wikipedia

    en.wikipedia.org/wiki/Convolution

    Download as PDF; Printable version; In other projects ... the convolution formula can be described as the area under the function ... 2D, [17] and 3D ...

  3. 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 *.

  4. 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.

  5. Diffusion equation - Wikipedia

    en.wikipedia.org/wiki/Diffusion_equation

    Download as PDF; Printable version ... The resulting diffusion algorithm can be written as an image convolution with a varying kernel (stencil) of size 3 × 3 in 2D ...

  6. Point spread function - Wikipedia

    en.wikipedia.org/wiki/Point_spread_function

    By virtue of the linearity property of optical non-coherent imaging systems, i.e., . Image(Object 1 + Object 2) = Image(Object 1) + Image(Object 2). the image of an object in a microscope or telescope as a non-coherent imaging system can be computed by expressing the object-plane field as a weighted sum of 2D impulse functions, and then expressing the image plane field as a weighted sum of the ...

  7. Dirichlet kernel - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_kernel

    The convolution of D n (x) with any function f of period 2 π is the nth-degree Fourier series approximation to f, i.e., we have () = () = = ^ (), where ^ = is the k th Fourier coefficient of f. This implies that in order to study convergence of Fourier series it is enough to study properties of the Dirichlet kernel.

  8. 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 ).

  9. 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.