Inverse Discrete Cosine Transform

The Inverse DCT

Usage

idct(y, n)

# S3 method for class 'numeric'
idct(y, n = length(y))

# S3 method for class 'matrix'
idct(y, n = nrow(y))

Arguments

y

A vector or matrix of DCT coefficients

n

The desired length of the idct

Value

The returned value depends on the values in y.

When passed a numeric vector, returns numeric vector of length n.

When passed a matrix, returns a matrix with n rows and the same number of columns as y.

Details

Applies the Inverse DCT (see dct for more details).

$$ x_j = \sqrt{2}y_0 + 2\sum_{k=1}^{N-1} y_k \cos\left(\frac{\pi k(2j+1)}{2J}\right) $$

Examples

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

dct_coefs <- dct(y)
recovered_y <- idct(dct_coefs)

plot(y, recovered_y)