DISCRETE COSINE TRANSFORM
\dɪskɹˈiːt kˈə͡ʊsa͡ɪn tɹansfˈɔːm], \dɪskɹˈiːt kˈəʊsaɪn tɹansfˈɔːm], \d_ɪ_s_k_ɹ_ˈiː_t k_ˈəʊ_s_aɪ_n t_ɹ_a_n_s_f_ˈɔː_m]\
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(DCT) A technique for expressing a waveform as aweighted sum of cosines.The DCT is central to many kinds of signal processing,especially video compression.Given data A(i), where i is an integer in the range 0 to N1,the forward DCT (which would be used e.g. by an encoder) is: B(k) = sum A(i) cos ( (pi k/N) (2 i + 1)/2) i=0 to N1B(k) is defined for all values of the frequencyspace variablek, but we only care about integer k in the range 0 to N1.The inverse DCT (which would be used e.g. by a decoder) is: AA(i)= sum B(k) (2delta(k0)) cos ( (pi k/N) (2 i + 1)/2) k=0 to N1where delta(k) is the Kronecker delta.The main difference between this and a discrete Fouriertransform (DFT) is that the DFT traditionally assumes thatthe data A(i) is periodically continued with a period of N,whereas the DCT assumes that the data is continued with itsmirror image, then periodically continued with a period of 2N.Mathematically, this transform pair is exact, i.e. AA(i) ==A(i), resulting in lossless coding; only when some of thecoefficients are approximated does compression occur.There exist fast DCT algorithms in analogy to the FastFourier Transform.
By Denis Howe
Word of the day
Piper Longum
 slender tropical climber of the eastern Himalayas As we receive the berries, they consist of unripe fruit dried in sun; and are small, round grains, disposed spirally on a cylindrical receptacle. stimulant, carminative, tonic, like other peppers. A shrub indigenous to Malabar, Ceylon, eastern Bengal, Timor, and the Philippines, cultivated in India for its fruits (see 2d def.).