On entry: the
$m$ Hermitian sequences must be stored consecutively in
x in Hermitian form. Sequence 1 should occupy the first
$n$ elements of
x, sequence 2 the elements
$n$ to
$2n-1$, so that in general sequence
$p$ occupies the array elements
$(p-1)n$ to
$pn-1$. If the
$n$ data values
${z}_{j}^{p}$ are written as
${x}_{j}^{p}+{iy}_{j}^{p}$, then for
$0\le j\le n/2$,
${x}_{j}^{p}$ should be in array element
${\mathbf{x}}\left[(p-1)\times n+j\right]$ and for
$1\le j\le (n-1)/2$,
${y}_{j}^{p}$ should be in array element
${\mathbf{x}}\left[(p-1)\times n+n-j\right]$.
On exit: the components of the
$m$ discrete Fourier transforms, stored consecutively. Transform
$p$ occupies the elements
$(p-1)n$ to
$pn-1$ of
x overwriting the corresponding original sequence; thus if the
$n$ components of the discrete Fourier transform are denoted by
${\hat{x}}_{\mathit{k}}^{p}$, for
$\mathit{k}=0,1,\dots ,n-1$, then the
$mn$ elements of the array
x contain the values