Discrete Cosine Transform

dct(X[, type=2])

: Replaces the columns of a dense real matrix with their discrete cosine transforms. The second argument, an integer between 1 and 4, denotes the type of transform (DCT-I, DCT-II, DCT-III, DCT-IV). The DCT-I transform requires that the row dimension of X is at least 2. These transforms are defined as follows (for a matrix with n rows).
$k n∑- 2 DCT -I: X [k,:] := X [0,:]+ (- 1)X [n - 1,:]+ 2 X[j,:]cos(πjk∕(n - 1)), k = 0,...,n - 1. j=1 n∑-1 DCT -II: X [k,:] := 2 X [j,:]cos(π(j + 1∕2)k∕n), k = 0,...,n - 1. j=0 n∑-1 DCT -III: X [k,:] := X [0,:]+ 2 X [j,:]cos(πj(k + 1∕2)∕n), k = 0,...,n - 1. j=1 n∑-1 DCT -IV: X [k,:] := 2 X [j,:]cos(π(j + 1∕2)(k + 1∕2)∕n), k = 0,...,n- 1. j=0$

idct(X[, type=2])

: Replaces the columns of a dense real matrix with the inverses of the discrete cosine transforms defined above.