The discrete cosine transform (DCT) matrix for a given dimension n is calculated.
dctMatrix(n)
| n | Dimension for the DCT matrix. |
|---|
The n-by-n DCT matrix.
The function can be used for 1D- or 2D-DCT transforms of data.
1D: Let Q be a m-by-n matrix with some data. D is a
m-by-m DCT matrix created by dctMatrix(m). Then D %*% Q returns the
discrete cosine transform of the columns of Q. t(D) %*% Q returns the
inverse DCT of the columns of Q. As D is orthogonal, solve(D) = t(D).
2D: Let Q be a m-by-n matrix with some data. D_m is a
m-by-m DCT matrix created by dctMatrix(m), D_n a n-by-n DCT matrix
created by dctMatrix(n). D_m %*% Q %*% t(D_n) computes the 2D-DCT
of Q. The inverse 2D-DCT of Q can be computed via
t(D_mm) %*% DCT_Q %*% D_n.
D_m transforms along columns, D_n along rows. Since D is orthogonal, solve(D) = t(D).
It can be faster to use dctMatrix than using a direct transformation,
especially when calculating several DCT's.
D <- dctMatrix(5)