Discrete Sine Transform

dst(X[, type=1])

: Replaces the columns of a dense real matrix with their discrete sine transforms. The second argument, an integer between 1 and 4, denotes the type of transform (DST-I, DST-II, DST-III, DST-IV). These transforms are defined as follows (for a matrix with n rows).
$n∑-1 DST -I: X[k,:] := 2 X [j,:]sin(π (j + 1)(k+ 1)∕(n+ 1)), k = 0,...,n - 1. j=0 n∑-1 DST -II: X[k,:] := 2 X [j,:]sin(π (j + 1∕2)(k+ 1)∕n), k = 0,...,n - 1. j=0 k n∑-2 DST-III: X[k,:] := (- 1)X [n- 1,:]+ 2 X [j,:]sin(π(j + 1)(k+ 1∕2)∕n), k = 0,...,n - 1. j=0 n∑-1 DST-IV: X[k,:] := 2 X [j,:]sin(π (j + 1∕2)(k+ 1∕2)∕n), k = 0,...,n - 1. j=0$

idst(X[, type=1])

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