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# complex_data

Keywords: complex numbers, frequency domain
```                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.