# scipy.fftpack.rfft¶

scipy.fftpack.rfft(x, n=None, axis=- 1, overwrite_x=False)[source]

Discrete Fourier transform of a real sequence.

Parameters
xarray_like, real-valued

The data to transform.

nint, optional

Defines the length of the Fourier transform. If n is not specified (the default) then `n = x.shape[axis]`. If `n < x.shape[axis]`, x is truncated, if `n > x.shape[axis]`, x is zero-padded.

axisint, optional

The axis along which the transform is applied. The default is the last axis.

overwrite_xbool, optional

If set to true, the contents of x can be overwritten. Default is False.

Returns
zreal ndarray

The returned real array contains:

```[y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2))]              if n is even
[y(0),Re(y(1)),Im(y(1)),...,Re(y(n/2)),Im(y(n/2))]   if n is odd
```

where:

```y(j) = sum[k=0..n-1] x[k] * exp(-sqrt(-1)*j*k*2*pi/n)
j = 0..n-1
```

Notes

Within numerical accuracy, `y == rfft(irfft(y))`.

Both single and double precision routines are implemented. Half precision inputs will be converted to single precision. Non-floating-point inputs will be converted to double precision. Long-double precision inputs are not supported.

To get an output with a complex datatype, consider using the newer function `scipy.fft.rfft`.

Examples

```>>> from scipy.fftpack import fft, rfft
>>> a = [9, -9, 1, 3]
>>> fft(a)
array([  4. +0.j,   8.+12.j,  16. +0.j,   8.-12.j])
>>> rfft(a)
array([  4.,   8.,  12.,  16.])
```