R: Discrete Trigonometric Transforms

dtt {dtt} | R Documentation

## Discrete Trigonometric Transforms

### Description

Performs univariate discrete sine, cosine or Hartley transform.

### Usage

    dtt(x, type = c("dct", "dst", "dht"), variant = 2, inverted = FALSE)
    dct(x, variant = 2, inverted = FALSE)
    dst(x, variant = 2, inverted = FALSE)
    dht(x, inverted = FALSE)

### Arguments

`x` | a vector or 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 vector of real numbers into a vector of its DCT, DST or DHT components, of the same length.

If the x is a matrix, the transform goes by rows (each row of a result is a transform of corresponding row in x).

The dct, dst and dht functions are simple wrappers for choosing the type by function name.

### Value

A transformed vector.

### Author(s)

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).

### See Also

`mvdtt`, `fft`, `mvfft`

### Examples

    x=seq(0,20,length=200)
    y=x*sin(x)+cos(x)+5*cos(10*x)+rnorm(200,sd=0.1)
    plot(y)
    z=dct(y); z[151:200]=0; lines(dct(z,inverted=TRUE),col=2);
    z=dct(y); z[21:200]=0; lines(dct(z,inverted=TRUE),col=4);

[Package dtt version 0.1-2 Index]