dpss(N, W, K [,First]), N >= 1, 1 <= K <= N, 1 <= First <= N - K + 1 integers, 0 < W < .5 |

dpss(N, W, K) computes Discrete Prolate Spheroidal Sequences (DPSS) with half bandwidth W for orders 0, 1, ..., K-1. The order L DPSS is the L+1-th orthonormal eigenvector of a certain tridiagonal symmetric matrix of order N (see below). The value returned is N by K REAL matrix, with the first K eigenvectors in columns 1, 2, ... K in order of decreasing eigenvalue. dpss(N, W, K, J) does the same, except the DPSS have orders J-1, J, ..., J+K-2, that is they are eigenvectors J, J+1, ..., J+K-1 of the tridiagonal matrix. It returns a N by K REAL matrix, with eigenvectors J, J+1,..., J+K-1 in columns 1, 2, ... K. N, K and J must be integers satisfying N >= 1, 1 <= K <= N, 1 <= J <= N - K + 1. W must be a REAL scalar, 0 < W < 0.5. Discrete Prolate Spheroidal Sequences (DPSS) are used as tapers (data windows) in multi-taper spectrum estamation. Their continuous Fourier transforms are very highly concentrated in low frequencies with a very sharp cutoff near frequencies W and -W cycles. Because they are eigenvectors of a symmetric matrix, they are orthogonal. The diagonal and subdiagonal of the tridiagonal matrix are d = cos(2*PI*W)*(.5*run(-N+1,N-1,2))^2 and e = (run(N-1)*run(N-1,1))/2 The DPSS are computed by trideigen(d,e,J,J+K-1,values:F), followed by certain sign changes. See regular topic trideigen().

Gary Oehlert 2003-01-15