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5.3 Discrete Sine Transform
dst(X[, type=1])
- Replaces the columns of a dense real matrix with their discrete
sine transforms. The second argument, an integer between 1 and 4,
denotes the type of transform (DST-I, DST-II, DST-III, DST-IV).
These transforms are defined as follows
(for a matrix with n rows).
![\begin{eqnarray*}
\mbox{DST-I:} \qquad
X[k,:] & := &
2 \sum_{j=0}^{n-1} X[j,:...
...n-1} X[j,:] \sin(\pi (j+1/2)(k+1/2)/n),
\qquad k=0,\ldots,n-1.
\end{eqnarray*}](img75.gif)
idst(X[, type=1])
- Replaces the columns of a dense real matrix with the inverses
of the discrete sine transforms defined above.
The separable discrete two dimensional sine transform first computes the corresponding one dimensional tranform along the columns of the matrix, followed by the one dimensional transform along the rows of the matrix.
dst2(X[, type=1])
-
Replaces a dense real matrix with the two dimensional discrete sine transform.
idst2(X[, type=1])
-
Replaces a dense real matrix with the inverse two dimensional discrete sine transform.