# numpy.fft.rfft¶

numpy.fft.rfft(a, n=None, axis=-1)

Compute the one-dimensional discrete Fourier Transform for real input.

This function computes the one-dimensional n-point discrete Fourier Transform (DFT) of a real-valued array by means of an efficient algorithm called the Fast Fourier Transform (FFT).

Parameters : a : array_like Input array n : int, optional Number of points along transformation axis in the input to use. If n is smaller than the length of the input, the input is cropped. If it is larger, the input is padded with zeros. If n is not given, the length of the input (along the axis specified by axis) is used. axis : int, optional Axis over which to compute the FFT. If not given, the last axis is used. out : complex ndarray The truncated or zero-padded input, transformed along the axis indicated by axis, or the last one if axis is not specified. The length of the transformed axis is n/2+1. IndexError : If axis is larger than the last axis of a.

numpy.fft
For definition of the DFT and conventions used.
irfft
The inverse of rfft.
fft
The one-dimensional FFT of general (complex) input.
fftn
The n-dimensional FFT.
rfftn
The n-dimensional FFT of real input.

Notes

When the DFT is computed for purely real input, the output is Hermite-symmetric, i.e. the negative frequency terms are just the complex conjugates of the corresponding positive-frequency terms, and the negative-frequency terms are therefore redundant. This function does not compute the negative frequency terms, and the length of the transformed axis of the output is therefore n/2+1.

When A = rfft(a), A contains the zero-frequency term, which must be purely real due to the Hermite symmetry.

If n is even, A[-1] contains the term for frequencies n/2 and -n/2, and must also be purely real. If n is odd, A[-1] contains the term for frequency A[(n-1)/2], and is complex in the general case.

If the input a contains an imaginary part, it is silently discarded.

Examples

```>>> np.fft.fft([0, 1, 0, 0])
array([ 1.+0.j,  0.-1.j, -1.+0.j,  0.+1.j])
>>> np.fft.rfft([0, 1, 0, 0])
array([ 1.+0.j,  0.-1.j, -1.+0.j])
```

Notice how the final element of the fft output is the complex conjugate of the second element, for real input. For rfft, this symmetry is exploited to compute only the non-negative frequency terms.

numpy.fft.ifftn

numpy.fft.irfft