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Lexikon


discrete cosine transform


(DCT) A technique for expressing a waveform as a weighted sum of cosines. The DCT is central to many kinds of ref="module.php?name=Lexikon&file=search&eid=1&query=signal processing">signal processing, especially video ref="module.php?name=Lexikon&file=search&eid=1&query=compression">compression. Given data A(i), where i is an integer in the range 0 to N-1, 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 N-1 B(k) is defined for all values of the frequency-space variable k, but we only care about integer k in the range 0 to N-1. The inverse DCT (which would be used e.g. by a decoder) is: AA(i)= sum B(k) (2-delta(k-0)) cos((pi k/N)(2 i + 1)/2) k=0 to N-1 where delta(k) is the ref="module.php?name=Lexikon&file=search&eid=1&query=Kronecker delta">Kronecker delta. The main difference between this and a {discrete Fourier transform} (DFT) is that the DFT traditionally assumes that the data A(i) is periodically continued with a period of N, whereas the DCT assumes that the data is continued with its mirror image, then periodically continued with a period of 2N. Mathematically, this transform pair is exact, i.e. AA(i) == A(i), resulting in ref="module.php?name=Lexikon&file=search&eid=1&query=lossless coding">lossless coding only when some of the coefficients are approximated does compression occur. There exist fast DCT ref="module.php?name=Lexikon&file=search&eid=1&query=algorithms">algorithms in analogy to the {Fast Fourier Transform}. (1997-03-10)

In addition suitable contents:
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ref="module.php?name=Lexikon&op=content&tid=2888">CT ] [ ref="module.php?name=Lexikon&op=content&tid=2900">cu ] [ ref="module.php?name=Lexikon&op=content&tid=2941">cy ] [ ref="module.php?name=Lexikon&op=content&tid=2976">D ] [ ref="module.php?name=Lexikon&op=content&tid=3006">data ] [ ref="module.php?name=Lexikon&op=content&tid=3117">DC ] [ ref="module.php?name=Lexikon&op=content&tid=3134">DCT ] [ ref="module.php?name=Lexikon&op=content&tid=3151">de ] [ ref="module.php?name=Lexikon&op=content&tid=3177">dec ] [ ref="module.php?name=Lexikon&op=content&tid=3196">decode ] [ ref="module.php?name=Lexikon&op=content&tid=3257">delta ] [ ref="module.php?name=Lexikon&op=content&tid=3343">DFT ] [ ref="module.php?name=Lexikon&op=content&tid=3371">diff ] [ ref="module.php?name=Lexikon&op=content&tid=3436">ding ] [ ref="module.php?name=Lexikon&op=content&tid=3470">disc ] [ ref="module.php?name=Lexikon&op=content&tid=3476">discrete Fourier transform ] [ ref="module.php?name=Lexikon&op=content&tid=3565">do ] [ ref="module.php?name=Lexikon&op=content&tid=3752">du ] [ ref="module.php?name=Lexikon&op=content&tid=3865">ec ] [ ref="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ref="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ref="module.php?name=Lexikon&op=content&tid=3946">eg ] [ ref="module.php?name=Lexikon&op=content&tid=4068">encode ] [ ref="module.php?name=Lexikon&op=content&tid=4069">encoder ] [ ref="module.php?name=Lexikon&op=content&tid=4148">er ] [ ref="module.php?name=Lexikon&op=content&tid=4171">es ] [ ref="module.php?name=Lexikon&op=content&tid=4199">et ] [ ref="module.php?name=Lexikon&op=content&tid=4404">fas ] [ ref="module.php?name=Lexikon&op=content&tid=4413">Fast Fourier Transform ] [ ref="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ref="module.php?name=Lexikon&op=content&tid=4520">file ] [ ref="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ref="module.php?name=Lexikon&op=content&tid=4727">for ] [ ref="module.php?name=Lexikon&op=content&tid=4786">forward ] [ ref="module.php?name=Lexikon&op=content&tid=4806">Fourier transform ] [ ref="module.php?name=Lexikon&op=content&tid=4828">fr ] [ ref="module.php?name=Lexikon&op=content&tid=4909">FT ] [ ref="module.php?name=Lexikon&op=content&tid=4983">G ] [ ref="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ref="module.php?name=Lexikon&op=content&tid=5134">gh ] [ ref="module.php?name=Lexikon&op=content&tid=5205">gn ] [ ref="module.php?name=Lexikon&op=content&tid=5430">gy ] [ ref="module.php?name=Lexikon&op=content&tid=5434">h ] [ ref="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ref="module.php?name=Lexikon&op=content&tid=5675">hm ] [ ref="module.php?name=Lexikon&op=content&tid=5681">hn ] [ ref="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ref="module.php?name=Lexikon&op=content&tid=5779">ht ] [ ref="module.php?name=Lexikon&op=content&tid=5931">id ] [ ref="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ref="module.php?name=Lexikon&op=content&tid=5986">iff ] [ ref="module.php?name=Lexikon&op=content&tid=6013">il ] [ ref="module.php?name=Lexikon&op=content&tid=6024">image ] [ ref="module.php?name=Lexikon&op=content&tid=6064">in ] [ ref="module.php?name=Lexikon&op=content&tid=6194">int ] [ ref="module.php?name=Lexikon&op=content&tid=6196">integer ] [ ref="module.php?name=Lexikon&op=content&tid=6407">inverse ] [ ref="module.php?name=Lexikon&op=content&tid=6413">io ] [ ref="module.php?name=Lexikon&op=content&tid=6446">iq ] [ ref="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ref="module.php?name=Lexikon&op=content&tid=6482">is ] [ ref="module.php?name=Lexikon&op=content&tid=6558">it ] [ ref="module.php?name=Lexikon&op=content&tid=6760">K ] [ ref="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ref="module.php?name=Lexikon&op=content&tid=6822">ki ] [ ref="module.php?name=Lexikon&op=content&tid=7023">ld ] [ ref="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ref="module.php?name=Lexikon&op=content&tid=7354">loss ] [ ref="module.php?name=Lexikon&op=content&tid=7356">lossless ] [ ref="module.php?name=Lexikon&op=content&tid=7410">lt ] [ ref="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ref="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ref="module.php?name=Lexikon&op=content&tid=7457">M ] [ ref="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ref="module.php?name=Lexikon&op=content&tid=7582">man ] [ ref="module.php?name=Lexikon&op=content&tid=7648">Mathematica ] [ ref="module.php?name=Lexikon&op=content&tid=7981">mirror ] [ ref="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ref="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ref="module.php?name=Lexikon&op=content&tid=8079">module ] [ ref="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ref="module.php?name=Lexikon&op=content&tid=8228">ms ] [ ref="module.php?name=Lexikon&op=content&tid=8384">N ] [ ref="module.php?name=Lexikon&op=content&tid=8386">na ] [ ref="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ref="module.php?name=Lexikon&op=content&tid=8472">ne ] [ ref="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ref="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ref="module.php?name=Lexikon&op=content&tid=8660">nl ] [ ref="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ref="module.php?name=Lexikon&op=content&tid=8787">nu ] [ ref="module.php?name=Lexikon&op=content&tid=8964">om ] [ ref="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ref="module.php?name=Lexikon&op=content&tid=9457">pe ] [ ref="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ref="module.php?name=Lexikon&op=content&tid=9908">pr ] [ ref="module.php?name=Lexikon&op=content&tid=9995">process ] [ ref="module.php?name=Lexikon&op=content&tid=10000">processing ] [ ref="module.php?name=Lexikon&op=content&tid=10253">query ] [ ref="module.php?name=Lexikon&op=content&tid=10319">range ] [ ref="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ref="module.php?name=Lexikon&op=content&tid=10385">re ] [ ref="module.php?name=Lexikon&op=content&tid=10589">rete ] [ ref="module.php?name=Lexikon&op=content&tid=10767">ro ] [ ref="module.php?name=Lexikon&op=content&tid=10914">rw ] [ ref="module.php?name=Lexikon&op=content&tid=11010">sc ] [ ref="module.php?name=Lexikon&op=content&tid=11150">se ] [ ref="module.php?name=Lexikon&op=content&tid=11376">si ] [ ref="module.php?name=Lexikon&op=content&tid=11389">sig ] [ ref="module.php?name=Lexikon&op=content&tid=11396">signal ] [ ref="module.php?name=Lexikon&op=content&tid=11525">sl ] [ ref="module.php?name=Lexikon&op=content&tid=11651">so ] [ ref="module.php?name=Lexikon&op=content&tid=11757">space ] [ ref="module.php?name=Lexikon&op=content&tid=11790">spec ] [ ref="module.php?name=Lexikon&op=content&tid=11934">st ] [ ref="module.php?name=Lexikon&op=content&tid=12133">su ] [ ref="module.php?name=Lexikon&op=content&tid=12165">sum ] [ ref="module.php?name=Lexikon&op=content&tid=12359">T ] [ 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