Sine transform:
For length $ N = 2 ^ p $ sequence of real numbers $ {x (n) | n = 1, 2, .., N} $, which is a sine transform
$X(k)=\sqrt\frac{2}{N}s(k)\sum_{i=1}^{N}x(n)sin(k(n-\frac{1}{2})\frac{pi}{N}, k=1,2 ,..., N$
Where $ s (k) = \ left {1, k = 1, 2, 3, .., N-1, 1 / \ sqrt (2) k = n $