56 research outputs found

    Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations

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    We present algorithms for the type-IV discrete cosine transform (DCT-IV) and discrete sine transform (DST-IV), as well as for the modified discrete cosine transform (MDCT) and its inverse, that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy. Asymptotically, the operation count is reduced from ~2NlogN to ~(17/9)NlogN for a power-of-two transform size N, and the exact count is strictly lowered for all N > 4. These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split radix algorithm). The improved algorithms for DST-IV and MDCT follow immediately from the improved count for the DCT-IV.Comment: 11 page

    Two dimensional symmetric and antisymmetric generalizations of sine functions

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    Properties of 2-dimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutation of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region FF of the real Euclidean space, and that they are discretely orthogonal when summed up over a lattice of any density in FF. Decomposability of the products of functions into their sums is shown by explicitly decomposing products of all types. The formalism is set up for Fourier-like expansions of digital data over 2-dimensional lattices in FF. Continuous interpolation of digital data is studied.Comment: 12 pages, 5 figure

    Production Capacity of a Mountain Meadow in Slovakia

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    Slovakia is rich in grassland ecosystem diversity due to its geological, geomorphologic and climatic conditions (Seffer et al. 2002). Grasslands make up to 81% of total agricultural land in the upland and mountain regions. They are regarded as basic sources of forage for cattle and sheep. During the last century, the utilisation of mineral fertilisers increased dramatically not only on arable land, but even on grassland in Europe (Hejcman et al. 2007). The objective of our 11-year trial was to compare the dry matter production of permanent grasslands at two levels of mineral nutrition under extreme climatic conditions of northern Slovakia

    A Vision System as a Sensor for an Intelligent Robot

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    A Unified Fast MDCT/MDST Computation in the Evenly Stacked Analysis/Synthesis System

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