Inverse Discrete Cosine Transform Acceleration

The second derivative of the Inverse DCT

Usage

idct_accel(y, n = length(y))

Arguments

y

DCT coefficients

n

The desired length of the idct

Value

A vector with the second derivative of the inverse DCT

Details

Returns the second derivative (acceleration) of the Inverse DCT (see dct for more details).

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

Examples

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

dct_coefs <- dct(y)
y_accel <- idct_accel(dct_coefs)

plot(y)

plot(y_accel)