Computes an inverse real 1- or 2-D FFT. Takes a packed format FFT as input.
x (NxK matrix or K-length vector) – data
y (LxM real matrix or M-length vector) –
rfftip() uses the Temperton prime factor FFT algorithm. This algorithm can
compute the inverse FFT of any vector or matrix whose dimensions can be
expressed as the product of selected prime number factors. GAUSS
implements the Temperton algorithm for any integer power of 2, 3, and 5,
and one factor of 7. Thus,
rfftip() can handle any matrix whose dimensions
can be expressed as:
If a dimension of x does not meet this requirement, it will be padded
with zeros to the next allowable size before the inverse FFT is
computed. Note that
rfftip() assumes the length (for vectors) or column
dimension (for matrices) of x is \(K-1\) rather than \(K\), since the last
element or column does not hold FFT information, but the Nyquist frequencies.
The sizes of x and y are related as follows: \(L\) will be the smallest prime factor product greater than or equal to \(N\), and \(M\) will be twice the smallest prime factor product greater than or equal to \(K-1\). This takes into account the fact that x contains both positive and negative frequencies in the row dimension (matrices only), but only positive frequencies, and those only in the first \(K-1\) elements or columns, in the length or column dimension.
It is up to the user to guarantee that the input will return a real
result. If in doubt, use
ffti(). Note, however, that
ffti() expects a full
FFT, including negative frequency information, for input.