# ifft

Compute the inverse discrete fourier transform of a (conj. sym.) complex spectrum using the inverse fft or dft algorithm.

Usage
`ifft(x, {, xtype, poffset, prange})`
x
complex spectrum vector or matrix; if x is a matrix an inverse transform is computed for each column
• The spectra stored in x must be the 1st half of conj. sym. spectra, because a `complex→real` version of the inverse transformation is used and the results are real numbered signals.
• Each spectrum consists of `N=nrow(x)/2` complex values. The transformation length is set to `L=2*(N-1)`
• If the transformation length `L` is a power of 2 (`L=2^M`), the inverse fft algorithm is used, otherwise the inverse dft is used.
xtype
select the complex number format of x (default=0)
 xtype=0 → cartesian `{ re, im, .. }` otherwise → polar `{ amp, phase, .. }`
poffset
offset in samples to the signal begin or the selected zero phase position (default=0); If this value is not equal 0, the phase values stored in x are locked (see fft) and must be transformed to normal phase values before the inverse ft-transform is performed.
prange
selects the range of phase values stored in x (default=0)
 prange=0 → `0 ≤ phase[i] < 2*pi` otherwise → `-pi ≤ phase[i] < pi`
• The arguments poffset and prange are ignored if xtype equals 0 (x in cartesian format).
Result
A matrix y with ncol(x) columns, where each column y[*,j] contains the result of the inverse transform (the real valued signal) of the column x[*,j]. Each signal vector y[*,j] consists of `L` (real) samples.