Discrete Cosine Transform

Discrete Cosine Transform

Usage

dct(x)

# S3 method for class 'numeric'
dct(x)

# S3 method for class 'matrix'
dct(x)

Arguments

x

A vector or matrix to which the discrete cosine transform is applied

Value

Returned value depends on x.

When passed a numeric vector, returns a numeric vector the same size as x with the DCT Coefficients.

When passed a matrix, returns a matrix the same size as x with the DCT Coefficients.

Details

The DCT definitions here are based on the python scipy.fft.dct definitions. Specifically this use:

# python code
scipy.fft.dct(x, norm = "forward", orthogonalize = True)

$$ y_k = \frac{1}{zN} \sum_{j=0}^{N-1}x_j\cos\left(\frac{\pi k(2j+1)}{2N}\right) $$

$$ z = \begin{cases} \sqrt{2}& \text{for }k=0\\ 1 & \text{for }k>0 \end{cases} $$

For the Inverse Discrete Cosine Transform, see idct.

Examples

x <- seq(0, 1, length = 10)
y <- 5 + x + (2 * (x^2)) + (-2 * (x^4))

dct_coefs <- dct(y)