Concepts inAlgorithm 749: fast discrete cosine transform
In-place algorithm
In computer science, an in-place algorithm (or in Latin in situ) is an algorithm which transforms input using a data structure with a small, constant amount of extra storage space. The input is usually overwritten by the output as the algorithm executes. An algorithm which is not in-place is sometimes called not-in-place or out-of-place. An algorithm is sometimes, informally, called in-place as long as it overwrites its input with its output.
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Power of two
In mathematics, a power of two means a number of the form 2 where n is an integer, i.e. the result of exponentiation with as base the number two and as exponent the integer n. In a context where only integers are considered, n is restricted to non-negative values, so we have 1, 2, and 2 multiplied by itself a certain number of times. Because two is the base of the binary numeral system, powers of two are common in computer science.
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Discrete cosine transform
A discrete cosine transform (DCT) expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at different frequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio and images (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations.
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Algorithm
In mathematics and computer science, an algorithm Listen/ˈælɡərɪðəm/ (originating from al-Khwārizmī, the famous mathematician Muḥammad ibn Mūsā al-Khwārizmī) is a step-by-step procedure for calculations. Algorithms are used for calculation, data processing, and automated reasoning. More precisely, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function.
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