MacAnova representation of complex data An unrestricted complex series (vector) of length N is represented as a REAL N by 2 matrix with the real and imaginary parts in columns 1 and 2. An unrestricted N by p complex matrix (p unrestricted complex series) is represented by a REAL N by 2*p matrix, with the real and imaginary parts of the j-th series in columns 2*j-1 and 2*j. A N by 2*p-1 matrix can be considered to represent p-1 complex series and 1 real series in the last column. When the series represents a frequency function evaluated at Nfreq frequencies, row k usually contains the values for frequency (k-1)/Nfreq cycles. A complex vector with Hermitian symmetry (a Hermitian series) {x(j)} of length N is represented as a REAL vector, say, hx, of length N with hx[1] = x(0) hx[j+1] = Re(x(j)), 1 <= j < N/2 hx[N+1-j] = Im(x(j), 1 <= j < N/2. hx[N/2+1] = x(N/2) (only when N is even). p Hermitian series are represented by the columns of a N by p matrix. When the series represents a frequency function evaluated at Nfreq frequencies, row 1 contains the value for frequency 0 and rows j and Nfreq+1-j contain the real and imaginary parts of the function at frequency (j-1)/Nfreq cycles. See also topic 'hermitian'.

Gary Oehlert 2003-01-15