# scipy.fftpack.rfft

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

  Discrete Fourier transform of a real sequence.

  Parameters:
    x array_like, real-valued

      The data to transform.

    n int, 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.

    axis int, optional

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

    overwrite_x bool, optional

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

  Returns:
    z real 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

  See also

  `fft`, `irfft`, `scipy.fft.rfft`

  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.])