. . . . "In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample."@en . "Em matem\u00E1tica, a transformada discreta de seno (DST, do ingl\u00EAs Discrete Sine Transform) \u00E9 a vers\u00E3o da transformada de seno para um dom\u00EDnio discreto. Na verdade, podem-se definir 4 tipos diferentes de DST, de acordo com crit\u00E9rios diversos; essas transformadas s\u00E3o denotadas DST1, DST2, DST3 e DST4 ou DST-I, DST-II, DST-III e DST-IV A recupera\u00E7\u00E3o da sequ\u00EAncia original pela aplica\u00E7\u00E3o da transformada inversa assume que a fun\u00E7\u00E3o f(t) \u00E9 nula para t < 0 e tamb\u00E9m que ela \u00E9 uma fun\u00E7\u00E3o \"\u00EDmpar\", no sentido de termos f(k) = - f(n-k) no intervalo considerado. A DST possui as propriedade not\u00E1veis de:"@pt . . . . . . . . . . . . . . . . "Die diskrete Sinustransformation (DST, englisch discrete sine transform) ist eine reellwertige, diskrete, lineare, orthogonale Transformation, die \u00E4hnlich wie der imagin\u00E4re Teil der diskreten Fouriertransformation (DFT) ein zeitdiskretes Signal vom Zeitbereich (bei Zeitsignalen) bzw. dem Ortsbereich (bei r\u00E4umlichen Signalen) in den Frequenzbereich transformiert. Sie ist eng verwandt mit der diskreten Kosinustransformation (DCT), basiert aber im Gegensatz auf der ungeraden Sinusfunktion."@de . . . . . . . . . . "Transformada discreta de seno"@pt . . . . . . . . "\u79BB\u6563\u6B63\u5F26\u53D8\u6362"@zh . . "13743"^^ . . . "Transformada sinus discreta"@ca . "Em matem\u00E1tica, a transformada discreta de seno (DST, do ingl\u00EAs Discrete Sine Transform) \u00E9 a vers\u00E3o da transformada de seno para um dom\u00EDnio discreto. Na verdade, podem-se definir 4 tipos diferentes de DST, de acordo com crit\u00E9rios diversos; essas transformadas s\u00E3o denotadas DST1, DST2, DST3 e DST4 ou DST-I, DST-II, DST-III e DST-IV Transformadas discretas, ao contr\u00E1rio das transformadas cont\u00EDnuas, aplicam-se n\u00E3o a fun\u00E7\u00F5es cont\u00EDnuas mas a amostras obtidas destas. A partir de uma fun\u00E7\u00E3o cont\u00EDnua f(t) obt\u00E9m-se uma sequ\u00EAncia de n valores f(k), sendo k um n\u00FAmero inteiro de 0 a n-1; a transformada discreta de seno da sequ\u00EAncia f(k) \u00E9 uma outra sequ\u00EAncia, que chamaremos S(k), dada pelas express\u00F5es de defini\u00E7\u00E3o. A sequ\u00EAncia original pode ser recuperada a partir da sequ\u00EAncia S(k) por meio das express\u00F5es de defini\u00E7\u00E3o da transforma\u00E7\u00E3o inversa. A amostragem deve ser executada sobre um intervalo de comprimento \u03C4, suficiente para que todas as componentes significativas de f(t) estejam representadas devidamente em f(k) (ver Taxa de amostragem); assume-se que o intervalo \u0394t entre as amostragens \u00E9 fixo. A recupera\u00E7\u00E3o da sequ\u00EAncia original pela aplica\u00E7\u00E3o da transformada inversa assume que a fun\u00E7\u00E3o f(t) \u00E9 nula para t < 0 e tamb\u00E9m que ela \u00E9 uma fun\u00E7\u00E3o \"\u00EDmpar\", no sentido de termos f(k) = - f(n-k) no intervalo considerado. A DST possui as propriedade not\u00E1veis de: \n* ser mais simples que a transformada discreta de Fourier e possuir propriedades similares, e assim se prestar melhor \u00E0 solu\u00E7\u00E3o de problemas de equa\u00E7\u00F5es diferenciais com condi\u00E7\u00F5es de contorno tais que a impliquem na presen\u00E7a de somente fun\u00E7\u00F5es \u00EDmpares na resposta \n* se aproximar assintoticamente da transformada de Karhunen-Lo\u00E8ve, que \u00E9, do ponto de vista te\u00F3rico, \u00F3tima sob v\u00E1rios aspectos importantes para o processamento digital de sinais, apresentando sobre esta a vantagem apreci\u00E1vel de ser independente da fun\u00E7\u00E3o de entrada."@pt . . . . "\u96E2\u6563\u6B63\u5F26\u8B8A\u63DB\uFF08DST for Discrete Sine Transform\uFF09\u662F\u4E00\u7A2E\u8207\u5085\u7ACB\u8449\u8B8A\u63DB\u76F8\u95DC\u7684\u8B8A\u63DB\uFF0C\u985E\u4F3C\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\uFF0C\u4F46\u662F\u53EA\u7528\u5BE6\u6578\u77E9\u9663\u3002\u96E2\u6563\u6B63\u5F26\u8B8A\u63DB\u76F8\u7576\u65BC\u9577\u5EA6\u7D04\u70BA\u5B83\u5169\u500D\uFF0C\u4E00\u500B\u5BE6\u6578\u4E14\u5947\u5C0D\u7A31\u8F38\u5165\u8CC7\u6599\u7684\u7684\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u7684\u865B\u6578\u90E8\u5206\uFF08\u56E0\u70BA\u4E00\u500B\u5BE6\u5947\u8F38\u5165\u7684\u5085\u7ACB\u8449\u8B8A\u63DB\u70BA\u7D14\u865B\u6578\u5947\u5C0D\u7A31\u8F38\u51FA\uFF09\u3002\u6709\u4E9B\u8B8A\u578B\u88E1\u5C07\u8F38\u5165\u6216\u8F38\u51FA\u79FB\u52D5\u534A\u500B\u53D6\u6A23\u3002 \u4E00\u7A2E\u76F8\u95DC\u7684\u8B8A\u63DB\u662F\u96E2\u6563\u9918\u5F26\u8B8A\u63DB\uFF0C\u76F8\u7576\u65BC\u9577\u5EA6\u7D04\u70BA\u5B83\u5169\u500D\uFF0C\u5BE6\u5076\u51FD\u6570\u7684\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u3002\u53C3\u8003DCT\u672C\u6587\u6709\u95DC\u908A\u754C\u689D\u4EF6\u548C\u4E0D\u540C\u7684DCT\u548CDST\u95DC\u806F\u7684\u4E00\u822C\u8A0E\u8AD6\u3002"@zh . . . . "Diskrete Sinustransformation"@de . "Die diskrete Sinustransformation (DST, englisch discrete sine transform) ist eine reellwertige, diskrete, lineare, orthogonale Transformation, die \u00E4hnlich wie der imagin\u00E4re Teil der diskreten Fouriertransformation (DFT) ein zeitdiskretes Signal vom Zeitbereich (bei Zeitsignalen) bzw. dem Ortsbereich (bei r\u00E4umlichen Signalen) in den Frequenzbereich transformiert. Sie ist eng verwandt mit der diskreten Kosinustransformation (DCT), basiert aber im Gegensatz auf der ungeraden Sinusfunktion. Anwendung der DST, wie auch der DCT, liegen bei der L\u00F6sung von partiellen Differentialgleichungen. Bei dem Videostandard H.265 kann die DST bei bestimmten Einstellungen zum Einsatz kommen. Im Gegensatz zur DCT besitzt die DST in den meisten F\u00E4llen keine wesentliche Anwendung im Bereich der Signalverarbeitung und Datenkompression."@de . . "La transformada sinuso\u00EFdal discreta (DST), dins l'\u00E0mbit de la matem\u00E0tica, \u00E9s una similar a la transformada discreta de Fourier (DFT), per\u00F2 utilitzant una matriu purament real . \u00C9s equivalent a les parts imagin\u00E0ries d'una DFT d'aproximadament el doble de la longitud, que opera sobre dades reals amb una simetria estranya (ja que la transformada de Fourier d'una funci\u00F3 real i senar \u00E9s imagin\u00E0ria i senar), on en algunes variants, l'entrada i/o la sortida, les dades es desplacen en mitja mostra. La DST est\u00E0 relacionada amb la transformada de cosinus discret (DCT), que \u00E9s equivalent a una DFT de funcions reals i parelles. Generalment, el DST es deriva del DCT substituint la condici\u00F3 de Neumann a x=0 per una condici\u00F3 de Dirichlet . Tant el DCT com el DST van ser descrits per T. Natarajan i el 1974. El DST de tipus I (DST-I) va ser descrit posteriorment per el 1976, i el DST de tipus II (DST-II) va ser descrit despr\u00E9s per HB Kekra i JK Solanka el 1978. Els DST s'utilitzen \u00E0mpliament per resoldre equacions diferencials parcials mitjan\u00E7ant , on les diferents variants del DST corresponen a condicions de l\u00EDmit senar/parell lleugerament diferents als dos extrems de la matriu. Formalment, la transformada sinuso\u00EFdal discreta \u00E9s una funci\u00F3 lineal i inversible F : R N -> R N (on R denota el conjunt de nombres reals ), o equivalentment una matriu quadrada N \u00D7 N . Hi ha diverses variants del DST amb definicions lleugerament modificades. Els N nombres reals x 0, x N \u2212 1 es transformen en els N nombres reals X 0, X N \u2212 1 segons una de les f\u00F3rmules: DST-I: DST-II: DST-III: DST-IV:"@ca . . . . . . "Discrete sine transform"@en . "1121307471"^^ . . . . . . . . . . "In mathematics, the discrete sine transform (DST) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using a purely real matrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry (since the Fourier transform of a real and odd function is imaginary and odd), where in some variants the input and/or output data are shifted by half a sample. A family of transforms composed of sine and sine hyperbolic functions exists. These transforms are made based on the natural vibration of thin square plates with different boundary conditions. The DST is related to the discrete cosine transform (DCT), which is equivalent to a DFT of real and even functions. See the DCT article for a general discussion of how the boundary conditions relate the various DCT and DST types. Generally, the DST is derived from the DCT by replacing the Neumann condition at x=0 with a Dirichlet condition. Both the DCT and the DST were described by Nasir Ahmed T. Natarajan and K.R. Rao in 1974. The type-I DST (DST-I) was later described by Anil K. Jain in 1976, and the type-II DST (DST-II) was then described by H.B. Kekra and J.K. Solanka in 1978."@en . "196095"^^ . . . . "\u96E2\u6563\u6B63\u5F26\u8B8A\u63DB\uFF08DST for Discrete Sine Transform\uFF09\u662F\u4E00\u7A2E\u8207\u5085\u7ACB\u8449\u8B8A\u63DB\u76F8\u95DC\u7684\u8B8A\u63DB\uFF0C\u985E\u4F3C\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\uFF0C\u4F46\u662F\u53EA\u7528\u5BE6\u6578\u77E9\u9663\u3002\u96E2\u6563\u6B63\u5F26\u8B8A\u63DB\u76F8\u7576\u65BC\u9577\u5EA6\u7D04\u70BA\u5B83\u5169\u500D\uFF0C\u4E00\u500B\u5BE6\u6578\u4E14\u5947\u5C0D\u7A31\u8F38\u5165\u8CC7\u6599\u7684\u7684\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u7684\u865B\u6578\u90E8\u5206\uFF08\u56E0\u70BA\u4E00\u500B\u5BE6\u5947\u8F38\u5165\u7684\u5085\u7ACB\u8449\u8B8A\u63DB\u70BA\u7D14\u865B\u6578\u5947\u5C0D\u7A31\u8F38\u51FA\uFF09\u3002\u6709\u4E9B\u8B8A\u578B\u88E1\u5C07\u8F38\u5165\u6216\u8F38\u51FA\u79FB\u52D5\u534A\u500B\u53D6\u6A23\u3002 \u4E00\u7A2E\u76F8\u95DC\u7684\u8B8A\u63DB\u662F\u96E2\u6563\u9918\u5F26\u8B8A\u63DB\uFF0C\u76F8\u7576\u65BC\u9577\u5EA6\u7D04\u70BA\u5B83\u5169\u500D\uFF0C\u5BE6\u5076\u51FD\u6570\u7684\u96E2\u6563\u5085\u7ACB\u8449\u8B8A\u63DB\u3002\u53C3\u8003DCT\u672C\u6587\u6709\u95DC\u908A\u754C\u689D\u4EF6\u548C\u4E0D\u540C\u7684DCT\u548CDST\u95DC\u806F\u7684\u4E00\u822C\u8A0E\u8AD6\u3002"@zh .