ifft

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

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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 3

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.

See also

fft, dft, dct, cepstrum, lpc, complex arithmetic

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