dtt (version 0.1-2)

dtt: 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?

Value

A transformed vector.

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.

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);