Inverse Discrete Cosine Transform Rate

The first derivative of the Inverse DCT

Usage

idct_rate(y, n = length(y))

Arguments

y

DCT coefficients

n

The desired length of the idct

Value

A vector with the first derivative of the inverse DCT

Details

Returns the first derivative (rate of change) of the Inverse DCT (see dct for more details).

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

Examples

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

dct_coefs <- dct(y)
y_rate <- idct_rate(dct_coefs)

plot(y)

plot(y_rate)