dtt {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?

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);