mvdtt: 2D Discrete Trigonometric Transforms In dtt: Discrete Trigonometric Transforms

Description

Performs multivariate (2D) discrete sine, cosine or Hartley transform.

Usage

 ```1 2 3 4``` ```mvdtt(x, type = c("dct", "dst", "dht"), variant = 2, inverted = FALSE) mvdct(x, variant = 2, inverted = FALSE) mvdst(x, variant = 2, inverted = FALSE) mvdht(x, inverted = FALSE) ```

Arguments

 `x` a matrix to be transformed `type` type of transform. Default "dct" is discrete cosine, "dst" is discrete sine and "dht" is discrete Hartley `variant` a transformation variant - 1...4 for DCT-I...DCT-IV or DST-I...DST-IV. Default is DCT-II or DST-II. Ignored when type = "dht" `inverted` if the inverted transform should be performed?

Details

This function transforms a matrix of real numbers into a matrix of its DCT, DST or DHT components, of the same dimensions. It is done by so-called row-matrix algorithm.

The mvdct, mvdst and mvdht functions are simple wrappers for choosing the type by function name.

Value

A transformed matrix.

Lukasz Komsta

References

1. N. Ahmed, T. Natarajan, and K. R. Rao, "Discrete Cosine Transform", IEEE Trans. Computers, 90-93, Jan 1974. 2. S. A. Martucci, "Symmetric convolution and the discrete sine and cosine transforms", IEEE Trans. Sig. Processing SP-42, 1038-1051 (1994). 3. R. V. L. Hartley, "A more symmetrical Fourier analysis applied to transmission problems," Proc. IRE 30, 144-150 (1942).

`dtt`, `fft`, `mvfft`
 ```1 2 3 4 5``` ```x = rnorm(100); dim(x) = c(10,10); x mvdct(x) mvdct(mvdct(x),inverted=TRUE) ```