dctMatrix {mrbsizeR}

Create a n-by-n discrete cosine transform matrix.

Description

The discrete cosine transform (DCT) matrix for a given dimension n is calculated.

Usage

dctMatrix(n)

Arguments

n

Dimension for the DCT matrix.

Details

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.

Value

The n-by-n DCT matrix.

Examples

D <- dctMatrix(5)