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# scipy.fftpack.rfft

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

  Discrete Fourier transform of a real sequence.

  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).conjugate()`.

  Parameters : | x : array_like, real-valued The data to tranform. 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.

  See also

  `fft`, `irfft`, `scipy.fftpack.basic`

  Notes

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

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