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Bateman transform; Fourier transform. Short-time Fourier transform; Gabor transform; Hankel transform; Hartley transform; Hermite transform; Hilbert transform. Hilbert–Schmidt integral operator; Jacobi transform; Laguerre transform; Laplace transform. Inverse Laplace transform; Two-sided Laplace transform; Inverse two-sided Laplace transform ...
The reciprocal transformation, some power transformations such as the Yeo–Johnson transformation, and certain other transformations such as applying the inverse hyperbolic sine, can be meaningfully applied to data that include both positive and negative values [10] (the power transformation is invertible over all real numbers if λ is an odd ...
Comparison of the effects of applying 2D affine and perspective transformation matrices on a unit square. Another type of transformation, of importance in 3D computer graphics, is the perspective projection. Whereas parallel projections are used to project points onto the image plane along parallel lines, the perspective projection projects ...
When data is convolved with a function with wide support, such as for downsampling by a large sampling ratio, because of the Convolution theorem and the FFT algorithm, it may be faster to transform it, multiply pointwise by the transform of the filter and then reverse transform it. Alternatively, a good filter is obtained by simply truncating ...
In mathematics, an integral transform is a type of transform that maps a function from its original function space into another function space via integration, where some of the properties of the original function might be more easily characterized and manipulated than in the original function space.
Therefore, the Fourier transform goes from one space of functions to a different space of functions: functions which have a different domain of definition. In general, ξ {\displaystyle \xi } must always be taken to be a linear form on the space of its domain, which is to say that the second real line is the dual space of the first real line.
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory .
The following is a list of Laplace transforms for many common functions of a single variable. [1] The Laplace transform is an integral transform that takes a function of a positive real variable t (often time) to a function of a complex variable s (complex angular frequency ).