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A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies. The DCT, first proposed by Nasir Ahmed in 1972, is a widely used transformation technique in signal processing and data compression .
Discrete cosine transform. Modified discrete cosine transform; Discrete Hartley transform; Discrete sine transform; Discrete wavelet transform; Hadamard transform (or, Walsh–Hadamard transform) Fast wavelet transform; Hankel transform, the determinant of the Hankel matrix; Discrete Chebyshev transform. Equivalent, up to a diagonal scaling, to ...
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Help ... Discrete cosine transform; Discrete Fourier transform;
Another coordinate-remapping approach was suggested for integrals of the form (), in which case one can use the transformation = [(+ ) /] to transform the integral into the form () where () = ( [(+) /]) /, at which point one can proceed identically to Clenshaw–Curtis quadrature for f as above. [12]
The sine-only expansion for equally spaced points, corresponding to odd symmetry, was solved by Joseph Louis Lagrange in 1762, for which the solution is a discrete sine transform. The full cosine and sine interpolating polynomial, which gives rise to the DFT, was solved by Carl Friedrich Gauss in unpublished work around 1805, at which point he ...
Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete-time Fourier transform and the Z-transform, from discrete time to continuous frequency, and the Fourier series, from continuous time to discrete frequency, are outside the class of discrete transforms. Classical signal processing ...
Transform coding is a type of data compression for "natural" data like audio signals or photographic images. The transformation is typically lossless (perfectly reversible) on its own but is used to enable better (more targeted) quantization , which then results in a lower quality copy of the original input ( lossy compression ).
By applying Euler's formula (= + ), it can be shown (for real-valued functions) that the Fourier transform's real component is the cosine transform (representing the even component of the original function) and the Fourier transform's imaginary component is the negative of the sine transform (representing the odd component of the ...