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# scipy.fftpack.rfft

`scipy.fftpack.``rfft`(x, n=None, axis=-1, overwrite_x=0)

  rfft(x, n=None, axis=-1, overwrite_x=0) -> y

  Return discrete Fourier transform of real sequence x.

  The returned real arrays 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

  Note that y(-j) = y(n-j).

  Optional input:
    n
      Defines the length of the Fourier transform. If n is not specified then n=x.shape[axis] is set. If n<x.shape[axis], x is truncated. If n>x.shape[axis], x is zero-padded.
    axis
      The transform is applied along the given axis of the input array (or the newly constructed array if n argument was used).
    overwrite_x
      If set to true, the contents of x can be destroyed.
  Notes:
    y == rfft(irfft(y)) within numerical accuracy.

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