This equation requires S to be an invertible matrix, i.e., an existence of S -1 . If we choose the sampling step in s-space, and in the r-space in a proper fashion, equations 11 and 10 will become the standard sine-DFT. For that, we need to set N = M, s i = i • ∆s, and r k = k • ∆r with ∆r = 2π/(N • ∆s) and i, k = 1, 2, . . . , N. In this case, the matrix S -1 will be S -1 = S T = F , i.e., the direct sine-DFT matrix, and S = F -1 = F T will be the inverse sine-DFT matrix. As a side note, we want to mention how to get a general case of DFT. One simply has to replace the elements of S -matrix with S ik = exp(i • s i r k ), where "i" is the imaginary unit (i 2 = -1). C. Pure weighted sine least-squares spectral analysis