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#### 15.5.216 fftb

`fftb(data [, axes, /allaxes])`

`fftb, data [, axes, /allaxes]`

Returns a discrete backward Fourier transform of the real `data` along the indicated `axes`. By default, the backward transform (from frequency space) is applied in the first dimension. The returned values are of type `double`. The subroutine form replaces `data` with the transformed version.

If `axes` is specified, then it is taken to contain the axes along which transformation is to be done. No axis may appear more than once. The axes need not be in any specific order. If `/allaxes` is specified, then all axes are treated. If neither `axes` nor `/allaxes` are specified, then the first axis is assumed. The data may have arbitrary positive dimensions.

The returned array has the same dimensions as `data`.

The `data` are assumed to be stored as ’half-complex’ sequences, in order of increasing frequency. For each frequency, first the real and then the imaginary part is given, except that no imaginary part is given for values that are always real, i.e., for frequency zero and (for even-length sequences) also for the highest represented frequency (equal to half of the sequence length).

Note that only one half of the relevant frequencies are represented in `data`, because the missing half can be constructed from the provided half by complex conjugation.

`x = fftb(y)` is the opposite of `y = fft(x)`, and ```x = fftb(y, /amplitudes)``` is the opposite of ```y = fft(x, /amplitudes)```.

The calculation speed of the algorithm depends strongly on the number of data points in the dimension in which the algorithm is applied. For quickest results, that number of data points should only have factors equal to small prime numbers, such as 2, 3, and 5.

Opposite: fft